Kansainvälisen valuuttarahaston (IMF) julkaisut

International Monetary Fund (IMF) eli Kansainvälinen valuuttarahasto perustettiin v. 1945 valvomaan 187 jäsenmaansa rahoitusjärjestelmiä ja edistämään rahoitusmarkkinoiden vakautta ja kansainvälistä kauppaa. IMF julkaisee kansainvälisiä maksutasetilastoja n. 200 maasta, ulkomaankaupan tilastotietoa, aikasarjoja v. 1948 lähtien ja valtiontalouden rahoitustilastoja sekä maakohtaisia raportteja. Painettuun kokoelmaan kuuluu vuosikertomuksia, kausijulkaisuja, tilastoja ja monografioita. Ne käsittelevät makrotaloutta, taloudellista kehitystä, rahoitusmarkkinoita, kansainvälistä taloutta ja valuuttamarkkinoita. Kokoelmassa on yhteensä n. 4342 nimekettä ja se karttuu jatkuvasti. Kokoelman vanhin julkaisu on vuodelta 1944. Suurin osa kokoelman julkaisuista on ilmestynyt v. 1995 - 2011. Sitä uudempia ei ole enää hankittu painettuina. Kokoelmaan kuuluu erilaisia vuosikirjoja pitkältä ajanjaksolta, kuten Annual report (1948 -), Annual Report on Exchange Arrangements (1990 -), Balance of payments statistics yearbook (1938 - ), Direction of trade statistics yearbook (1958 - ), Government finance statistics yearbook (1952 - ) ja International financial statistics yearbook (1991 - ). Kokoelma sisältää myös kausijulkaisuja kuten Economic review (1951 - ), IMF staff papers (1951 -) ja International financial statistics (1948 -). Kokoelmaan kuuluvat myös elektronisia julkaisuja sisältävät IMF E-Library ja AREAER -tietokannat. AREAR-tietokannassa on Annual Report on Exchange Arrangements -julkaisut sähköisessä muodossa. Tietokannassa on dataa mm. IMF:n jäsenmaiden valuutta- ja kauppajärjestelyistä. IMF E-Library, sisältää elektronisia julkaisuja sekä tilastotietokannat: International financial statistics (IFS), Balance of payments statistics (BOP), Direction of trade statistics (DOT) ja Government finance statistics (GFS). Julkaisuja on yhteensä n. 11 806. Kokoelman uudempaa osaa säilytetään Suomen Pankin kirjaston avokokoelmassa ja vanhempaa varastokokoelmassa. Painetut julkaisut ovat käytettävissä kirjastossa ja lainattavissa lukuun ottamatta tilastojulkaisuja, kausijulkaisuja ja vuosikirjoja. Elektronisia tietokantoja voi käyttää vain organisaation henkilökunta.

Structure-related magnetic fabric studies : implications for deformed and undeformed Precambrian rocks

The aim of this thesis research was to gain a better understanding of the emplacement of rapakivi granite intrusions, as well as the emplacement of gold-bearing hydrothermal fluids in structurally controlled mineralizations. Based on investigations of the magnetic fabric, the internal structures could be analysed and the intrusion mechanisms for rapakivi granite intrusions and respectively different deformation stages within gold-bearing shear and fault zones identified. Aeromagnetic images revealed circular structures within the rapakivi granite batholiths of Wiborg, Vehmaa and Åland. These circular structures represent intrusions that eventually build up these large batholiths. The rapakivi granite intrusions of Vehmaa, Ruotsinpyhtää within the Wiborg batholith and Saltvik intrusions within the Åland batholith all show bimodal magnetic susceptibilities with paramagnetic and ferromagnetic components. The distribution of the bimodality is related to different magma batches of the studied intrusions. The anisotropy of magnetic susceptibility (AMS) reveals internal structures that cannot be studied macroscopically or by microscope. The Ruotsinpyhtää and Vehmaa intrusions represent similar intrusion geometries, with gently to moderately outward dipping magnetic foliations. In the case of Vehmaa, the magnetic lineations are gently plunging and trend in the directions of the slightly elongated intrusion. The magnetic lineations represent magma flow. The shapes of the AMS ellipsoids are also more planar (oblate) in the central part of the intrusion, whereas they become more linear (prolate) near the margin. These AMS results, together with field observations, indicate that the main intrusion mechanism has involved the subsidence of older blocks with successive intrusion of fractionated magma during repeated cauldron subsidence. The Saltvik area within the Åland batholith consists of a number of smaller elliptical intrusions of different rapakivi types forming a multiple intrusive complex. The magnetic fabric shows a general westward dipping of the pyterlite and eastward dipping of the contiguous even-grained rapakivi granite, which indicates a central inflow of magma batches towards the east and west resulting from a laccolitic emplacement of magma batches, while the main mechanism for space creation was derived from subsidence. The magnetic fabric of structurally controlled gold potential shear and fault zones in Jokisivu, Satulinmäki and Koijärvi was investigated in order to describe the internal structures and define the deformation history and emplacement of hydrothermal fluids. A further aim of the research was to combine AMS studies with palaeomagnetic methods to constrain the timing for the shearing event relative to the precipitation of ferromagnetic minerals and gold. All of the studied formations are dominated by monoclinic pyrrhotite. The AMS directions generally follow the tectonic structures within the formations. However, internal variations in the AMS direction as well as the shapes of the AMS ellipsoids are observed within the shear zones. In Jokisivu and Satulinmäki in particular, the magnetic signatures of the shear zone core differ from the margins. Furthermore, the shape of the magnetic fabric in the shear zone core of Jokisivu is dominated by oblate shapes, whereas the margins exhibit prolate shapes. These variations indicate a later effect of the hydrothermal fluids on the general shear event. The palaeo-magnetic results reveal a deflection from the original Svecofennian age geomagnetic direction. These results, coupled with correlations between the orientation of the NRM vectors and the magnetic and rock fabrics, imply that the gold-rich hydrothermal fluids were emplaced pre/syntectonically during the late stages of the Svecofennian orogeny.

Opportunities, constraints and constrained opportunities – A study on mothers’ working time patterns in 22 European countries

The aim of this study was to analyse mothers’ working time patterns across 22 European countries. The focus was on three questions: how much mothers prefer to work, how much they actually work, and to what degree their preferred and actual working times are (in)consistent with each other. The focus was on cross-national differences in mothers’ working time patterns, comparison of mothers’ working times to that of childless women and fathers, as well as on individual- and country-level factors that explain the variation between them. In the theoretical background, the departure point was an integrative theoretical approach where the assumption is that there are various kinds of explanations for the differences in mothers’ working time patterns – namely structural, cultural and institutional – , and that these factors are laid in two levels: individual- and country-levels. Data were extracted from the European Social Survey (ESS) 2010 / 2011. The results showed that mothers’ working time patterns, both preferred and actual working times, varied across European countries. Four clusters were formed to illustrate the differences. In the full-time pattern, full-time work was the most important form of work, leaving all other working time forms marginal. The full-time pattern was perceived in terms of preferred working times in Bulgaria and Portugal. In polarised pattern countries, fulltime work was also important, but it was accompanied by a large share of mothers not working at all. In the case of preferred working times, many Eastern and Southern European countries followed it whereas in terms of actual working times it included all Eastern and Southern European countries as well as Finland. The combination pattern was characterised by the importance of long part-time hours and full-time work. It was the preferred working time pattern in the Nordic countries, France, Slovenia, and Spain, but Belgium, Denmark, France, Norway, and Sweden followed it in terms of actual working times. The fourth cluster that described mothers’ working times was called the part-time pattern, and it was illustrated by the prevalence of short and long part-time work. In the case of preferred working times, it was followed in Belgium, Germany, Ireland, the Netherlands and Switzerland. Besides Belgium, the part-time pattern was followed in the same countries in terms of actual working times. The consistency between preferred and actual working times was rather strong in a majority of countries. However, six countries fell under different working time patterns when preferred and actual working times were compared. Comparison of working mothers’, childless women’s, and fathers’ working times showed that differences between these groups were surprisingly small. It was only in part-time pattern countries that working mothers worked significantly shorter hours than working childless women and fathers. Results therefore revealed that when mothers’ working times are under study, an important question regarding the population examined is whether it consists of all mothers or only working mothers. Results moreover supported the use of the integrative theoretical approach when studying mothers’ working time patterns. Results indicate that mothers’ working time patterns in all countries are shaped by various opportunities and constraints, which are comprised of structural, cultural, institutional, and individual-level factors.

Evolution of an Archean greenstone belt in the Stormy Lake - Kawashegamuk Lake area (stratigraphy, structure and geochemistry) - Western Wabigoon Subprovince, Northwest Ontario /

330 km 2 of the easter-n part of the Archean Manitou Lakes - Stormy Lake metavolcanic - metasedimentary belt have been mapped and sampled. A large number of rocks ~.vere analyzed for the major and trace constituents including the rare-earth elements (REE). The Stormy Lake - Kawashegamuk Lake area may be subdivided into four major lithological groups of supracrustal rocks 1) A north-facing mafic assemblage, consisting of pillowed tholeiitic basalts and gabbro sills characterized by flat REE profiles, is exposed in the south part of the map area and belongs to a 8000 m thick homoclinal assemblage outside the map area. Felsic pyroclastic rocks believed to have been issued from a large central vent conformably overlie the tholeiites. 2) A dominantly epiclastic group facing to the north consists of terrestrial deposits interpreted to be an alluvial fan deposit ; a submarine facies is represented by turbiditic sediments. 3) The northeastern part of the study area consists of volcanic rocks belonging to two mafic - felsic cycles facing to the southuest ; andesitic flows with fractionated REE patterns make up a large part of the upper cycle, whereas the lower cycle has a stronger chemical polarity being represented by tholeiitic flows, with flat REE, which a r e succeeded by dacitic and rhyolitic pyroclasti cs. iii 4) A thick monotonous succession of tholeiitic pillmled basalt f lows and gabbro sills with flat REE represent the youngest supracrustal rocks. TIle entire belt underwent folding, faulting and granitic plutonism during a tectono-thermal event around 2700 Ma ago. Rocks exposed in the map area were subjected to regional greenschist facies metamorphism, but higher metamorphic grades are present near late granitic intrusions. Geochemical studies have been useful in 1) distinguishing the various rock units ; 2) relating volcanic and intrusive rocks 3) studying the significance of chemical changes due to post magmatic processes 4) determining the petrogenesis of the major volcanic rock types. In doing so, two major volcanic suites have been recognized : a) a tholeiitic suite, mostly represented by mafic rocks, was derived from partial melting of upper mantle material depleted in Ti, K and the light REE ; b) a calc-alkalic suite which evolved from partial melting of amphibolite in the lower crust. The more differentiated magma types have been produced by a multistage process involving partial melting and fractional crystallization to yield a continuum of compos i t i ons ranging from basaltic andesite to rhyolite. A model for the development of the eastern part of the Manitou Lakes - Stormy Lake belt has been proposed.

Geology of the Rankin Inlet area, Northwest Territories /

The Rankin Inlet area, on the west shore of Hudson Bay in the Northwest Territories, is in the Churchill Structural Province. Metamorphosed volcanic and sedimentary rocks, previously mapped as Archean and part of the Kaminak Group, underlie most of the area. The Rankin Inlet Group consists of greywacke, with minor conglomeratic greywacke, quartzite and dolomite, overlain by massive and pillowed basaltic flows. Gabbro sills intrude the sediments near the base of the volcanic sequence and three serpentinite sills outcrop at the base of the volcanic sequence. The sediments are in fault-contact with quartz monzonite to the south and were intruded by granitic rocks to the northwest. Two periods of folding were defined by the mapping. The first generation folds are recumbent isoclinal folds, with northwest-trending and northeast-dipping axial planes, formed through gravitational sliding. The second generation folds are symmetrically disposed about the axis of the granitic intrusion and have east-southeast trending and nearly vertical axial planes. Whole-rock analysis of 64 rock samples indicates that metasomatic alteration accompanied the intrusion of both the granitic rocks and the serpentinite. The volcanic rocks, gabbro and serpentinite were derived from a magma of oceanic tholeiitic affinities. The stratigraphic sequence and chemistry of the volcanic rocks of the Rankin Inlet Group indicate that this assemblage is correlative with the Hurwitz Group rather than the Kaminak Group and is therefore Aphebian in age.

A reconnaissance study of the metamorphic petrology and volcanic geochemistry of a portion of the Island Lake greenstone belt, Manitoba /

The Island Lake greenstone belt is one of the major Archean supracrustal exposures in the northwestern part of the Superior Province of the Canadian Shield. This belt is subdivided into two units: 1) a lower sequence characterised by pillowed to massive, locally pyroclastic, basalt to andesite with a thin central zone of felsic derivatives, all of which are interbedded with and overlain by thick sequences of turbidite facies rock; 2) the upper unit which consists of thick stratified conglomerate overlain by thickly bedded arkose and feldspathic greywacke. Reconnaissance sampling traverses were completed across both the strike of the belt and along its margins with adjacent granitoids. Most of the belt is within the greenschist metamorphic f acies with amphibolite facies occurring in certain areas near t he margins. A post-tectonic, low pressure thermal event may be responsible for the development of a unit of cordierite schi s t which stretches southeastwards from the east end of Cochrane Bay. Volcanism is cyclical in nature changing from tholeiitic to calc-alkaline. There is a general progression in the character of the lavas from mafic t o felsic with stratigraphic height. Chemica l d a ta sugges t that h i gh level fractionation of a mantle- derived ' dry' magma i s t he s ource of the thole i iti c lavas. Contamination of this magma with 'we t' sia l and subsequent fractionation may be r esponsi b l e for the calcalkaline phases .Observations of stratigraphic relationships (in particular the contact between the supracrustals and the granitoids) coupled with the metamorphic and chemical studies, allow the construction of a preliminary model for the evolution of the Island Lake greenstone belt. The following sequential development is suggested: 1) a platform stage characterised by the subaqueous effusion of mafic to intermediate lavas of alternating tholeiitic and calc-alkaline affinities; 2) an edifice stage marked by the eruption of felsic calc-alkaline rocks; 3) an erosional stage characterised by the deposit~on of thick sequences of turbidite facies rocks; 4) the impingement of granitic masses into the margins of the greenstone belt, which was probably related to a downward warping of the supracrustal pilei 5) the erosion of sialic massifs surrounding and within the greenstone belt and of early supracrustal piles, to give the clastic upper unit.

Petrography, geochemistry and structure of the Timmins area, Ontario

Regional structural analysis of the Timmins area indicates four major periods of tectonic deformation. The DI deformation is characterized by a series of isoclinal FI folds which are outlined in the study area by bedding, pillow tops and variolitic flows. The D2 deformation developed the Porcupine Syncline and refolded the Fl folds about a NE. axis. A pervasive S2 foliation developed during low grade (greenschist) regional metamorphism associated with the D2 deformation. The S2 foliation developed south of the Destor-Porcupine Break. The third phase of tectonic D3 deformation is recognized by the development of a S3 sub-horizontal crenulation cleavage which developed on the plane of the S2 foliation. No meso scopic folds are associated with this deformation. The 8 3 crenulation cleavage is observed south of the Destor-Porcupine Break. The D4 tectonic deformation is recorded as a subvertical S4 crenulation cleavage which developed on the plane of the S2 foliation and also offsets the S3 crenulation cleavage. Macroscopic F4 folds have refolded the F2 axial plane. No metamorphic recrystallization is associated with this deformation. The S4 crenulation cleavage is observed south of the Destor-Porcupine Break. Petrographic evidence indicates that the Timmins area has been subjected to pervasive regional low grade (greenschist) metamorphism which has recrystallized the original mineralogy. South of the study are~ the Donut Lake ultramafic lavas have been subjected to contact medium grade (amphibolite facies) metamorphism associated with the intrusion of the Peterlong Lake Complex. The Archean volcanic rocks of the Timmins area have been subdivided into komatiitic, tholeiitic and calcalkaline suites based on Zr, Ti0 2 and Ni. The three elements were used because of their r e lative immobility during subsequent metamorphic events. Geochemical observations in the Timmins area indicates that the composition of the Goose Lake and Donut Lake Formations are a series of peridotitic, pyroxenitic and basaltic komatiites. The Lower Schumacher Formation is a sequence of basaltic komatiites while the upper part of the Lower Schumacher Formation is an intercalated sequence of basaltic komatiites and low Ti0 2 tholeiites. The variolitic flows are felsic tholeiites in composition and geochemical evidenc e sugg ests that they developed as a n immiscible splitting of a tholeiitic magma. The Upper Schumacher Formation is a sequence of tholeiitic rocks dis p laying a mild iron enrichment. The Krist and Boomerang Formations are the felsic calc-alkaline rocks of the study area which are characteristically pyroclastic. The Redstone Fo rmation is dominantly a calc-alkali ne sequence of volcani c rocks whose minor mafic end me mbers exposed in 1t.he study hav e basaltic komatiitic compositions. Geochemical evidence sugges ts that the Keewatin-type se dimentary rocks have a composition similar to a quartz diorite or a granodiorite. Fi e l d obs ervations and petrographic evidence suggests that they were derived fr om a distal source and now repr esent i n part a turbidite sequence. The Timiskaming-type sedimentary rocks approach the c omp osi t ion of the felsic calc-alkaline rocks of the study area . The basal conglomerate in the study are a sugge s ts that th e uni t was derived fr om a proximal source. Petrographic and ge ochemical evidence suggests that the peridotitic and pyroxenitic komatiites originated as a 35-55% partial melt within the mantle, in excess of 100 Km. depth. The melt ros e as a diapir with the subsequent effusion of the ultramafic lavas, The basaltic komatiites and tholeiitic rocks originated in the mantle from lesser degrees of partial melting and fractionated in low pressure chambers. Geochemical evidence suggests a "genetic link" between the basaltic komatiites and tholeiites, The calc-alkaline rocks developed as a result of the increa.se In PO in the magma chamber. The felsic calcalkaline rocks are a late stage effusion possibly the last major volcanic eruptions in the area.

Physical volcanology, sedimentology, stratigraphy and petrochemistry of the Berry Creek metavolcanics: an Archean calc-alkaline complex, Lake of the Woods, Ontario

The steeply dipping, isoclinally folded early Precambrian (Archean) Berry Creek Metavolcanic Complex comprises primary to resedimented pyroclastic, epiclastic and autoclastic deposits. Tephra erupted from central volcanic edifices was dumped by mass flow mechanisms into peripheral volcanosedimentary depressions. Sedimentation has been essentially contemporaneous with eruption and transport of tephra. The monolithic to heterolithic tuffaceous horizons are interpreted as subaerial to subaqueous pumice and ash flows, secondary debris flows, lahars, slump deposits and turbidites. Monolithic debris flows, derived from crumble breccia and dcme talus, formed during downslope collapse and subsequent gravity flowage. Heterolithic tuff, lahars and lava flow morphologies suggest at least temporary emergence of the edifice. Local collapse may have accompanied pyroclastic volcanism. The tephra, produced by hydromagmatic to magmatic eruptions, were rapidly transported, by primary and secondary mechanisms, to a shallow littoral to deep water subaqueous fan developed upon the subjacent mafic metavolcanic platform. Deposition resulted from traction, traction carpet, and suspension sedimentation from laminar to turbulent flows. Facies mapping revealed proximal (channel to overbank) to distal facies epiclastics (greywackes, argillite) intercalated with proximal vent to medial fan facies crystal rich ash flows, debris flows, bedded tuff and shallow water to deep water lava flows. Framework and matrix support debris flows exhibit a variety of subaqueous sedimentary structures, e.g., coarse tail grading, double grading, inverse to normal grading, graded stratified pebbly horizons, erosional channels. Pelitic to psammitic AE turbidites also contain primary stru~tures, e.g., flames, load casts, dewatering pipes. Despite low to intermediate pressure greenschist to amphibolite grade metamorphism and variably penetrative deformation, relicts of pumice fragments and shards were recognized as recrystallized quartzofeldspathic pseudomorphs. The mafic to felsic metavolcanics and metasediments contain blasts of hornblende, actinolite, garnet, pistacitic epidote, staurolite, albitic plagioclase, and rarely andalusite and cordierite. The mafic metavolcanics (Adams River Bay, Black River, Kenu Lake, Lobstick Bay, Snake Bay) display _holeiitic trends with komatiitic affinities. Chemical variations are consistent with high level fractionation of olivine, plagioclase, amphibole, and later magnetite from a parental komatiite. The intermediate to felsic (64-74% Si02) metavolcanics generally exhibit calc-alkaline trends. The compositional discontinuity, defined by major and trace element diversity, can be explained by a mechanism involving two different magma sources. Application of fractionation series models are inconsistent with the observed data. The tholeiitic basalts and basaltic andesites are probably derived by low pressure fractionation of a depleted (high degree of partial melting) mantle source. The depleted (low Y, Zr) calc-alkaline metavolcanics may be produced by partial melting of a geochemically evolved source, e.g., tonalitetrondhjemite, garnet amphibolite or hydrous basalt.

Les tiers, vecteurs du réseau social. Les personnes et les biens dans le Code civil du Québec.

Un résumé en anglais est également disposnible.

National Application of International Law: The Statutory Interpretation Perspective

Reprinted with permission of the Publisher from The Canadian Yearbook of Internation Law, 41 by Don McRae © University of British Columbia Press 2003. All rights reserved.

Computation of locally free class groups

We show that the locally free class group of an order in a semisimple algebra over a number field is isomorphic to a certain ray class group. This description is then used to present an algorithm that computes the locally free class group. The algorithm is implemented in MAGMA for the case where the algebra is a group ring over the rational numbers.

Computing Generators of Free Modules over Orders in Group Algebras

Let E be a number field and G be a finite group. Let A be any O_E-order of full rank in the group algebra E[G] and X be a (left) A-lattice. We give a necessary and sufficient condition for X to be free of given rank d over A. In the case that the Wedderburn decomposition E[G] \cong \oplus_xM_x is explicitly computable and each M_x is in fact a matrix ring over a field, this leads to an algorithm that either gives elements \alpha_1,...,\alpha_d \in X such that X = A\alpha_1 \oplus ... \oplusA\alpha_d or determines that no such elements exist. Let L/K be a finite Galois extension of number fields with Galois group G such that E is a subfield of K and put d = [K : E]. The algorithm can be applied to certain Galois modules that arise naturally in this situation. For example, one can take X to be O_L, the ring of algebraic integers of L, and A to be the associated order A(E[G];O_L) \subseteq E[G]. The application of the algorithm to this special situation is implemented in Magma under certain extra hypotheses when K = E = \IQ.

Computations in Relative Algebraic K-Groups

Let G be finite group and K a number field or a p-adic field with ring of integers O_K. In the first part of the manuscript we present an algorithm that computes the relative algebraic K-group K_0(O_K[G],K) as an abstract abelian group. We solve the discrete logarithm problem, both in K_0(O_K[G],K) and the locally free class group cl(O_K[G]). All algorithms have been implemented in MAGMA for the case K = \IQ. In the second part of the manuscript we prove formulae for the torsion subgroup of K_0(\IZ[G],\IQ) for large classes of dihedral and quaternion groups.

Ein Algorithmus zur numerischen Verifikation der äquivarianten Tamagawazahlvermutung für eine Familie von Zahlkörpererweiterungen

Sei $N/K$ eine galoissche Zahlkörpererweiterung mit Galoisgruppe $G$, so dass es in $N$ eine Stelle mit voller Zerlegungsgruppe gibt. Die vorliegende Arbeit beschäftigt sich mit Algorithmen, die für das gegebene Fallbeispiel $N/K$, die äquivariante Tamagawazahlvermutung von Burns und Flach für das Paar $(h^0(Spec(N), \mathbb{Z}[G]))$ (numerisch) verifizieren. Grob gesprochen stellt die äquivariante Tamagawazahlvermutung (im Folgenden ETNC) in diesem Spezialfall einen Zusammenhang her zwischen Werten von Artinschen $L$-Reihen zu den absolut irreduziblen Charakteren von $G$ und einer Eulercharakteristik, die man in diesem Fall mit Hilfe einer sogenannten Tatesequenz konstruieren kann. Unter den Voraussetzungen 1. es gibt eine Stelle $v$ von $N$ mit voller Zerlegungsgruppe, 2. jeder irreduzible Charakter $\chi$ von $G$ erfüllt eine der folgenden Bedingungen 2a) $\chi$ ist abelsch, 2b) $\chi(G) \subset \mathbb{Q}$ und $\chi$ ist eine ganzzahlige Linearkombination von induzierten trivialen Charakteren; wird ein Algorithmus entwickelt, der ETNC für jedes Fallbeispiel $N/\mathbb{Q}$ vollständig beweist. Voraussetzung 1. erlaubt es eine Idee von Chinburg ([Chi89]) umzusetzen zur algorithmischen Berechnung von Tatesequenzen. Dabei war es u.a. auch notwendig lokale Fundamentalklassen zu berechnen. Im höchsten zahm verzweigten Fall haben wir hierfür einen Algorithmus entwickelt, der ebenfalls auf den Ideen von Chinburg ([Chi85]) beruht, die auf Arbeiten von Serre [Ser] zurück gehen. Für nicht zahm verzweigte Erweiterungen benutzen wir den von Debeerst ([Deb11]) entwickelten Algorithmus, der ebenfalls auf Serre's Arbeiten beruht. Voraussetzung 2. wird benötigt, um Quotienten aus den $L$-Werten und Regulatoren exakt zu berechnen. Dies gelingt, da wir im Fall von abelschen Charakteren auf die Theorie der zyklotomischen Einheiten zurückgreifen können und im Fall (b) auf die analytische Klassenzahlformel von Zwischenkörpern. Ohne die Voraussetzung 2. liefern die Algorithmen für jedes Fallbeispiel $N/K$ immer noch eine numerische Verifikation bis auf Rechengenauigkeit. Den Algorithmus zur numerischen Verifikation haben wir für $A_4$-Erweiterungen über $\mathbb{Q}$ in das Computeralgebrasystem MAGMA implementiert und für 27 Erweiterungen die äquivariante Tamagawazahlvermutung numerisch verifiziert.

Notas de viaje : volcanes

En la cub. precede al t??t.: Proyecto Educativo GENESIS : Asturias