A survey on recent p-adic integration theories and arithmetic applications

"Vegeu el resum a l'inici del document del fitxer adjunt."

Exact algorithms for p-adic fields and epsilon constant conjectures

We develop several algorithms for computations in Galois extensions of p-adic fields. Our algorithms are based on existing algorithms for number fields and are exact in the sense that we do not need to consider approximations to p-adic numbers. As an application we describe an algorithmic approach to prove or disprove various conjectures for local and global epsilon constants.

Indecomposable and noncrossed product division algebras over function fields of smooth p-adic curves

We construct indecomposable and noncrossed product division algebras over function fields of connected smooth curves X over Z(p). This is done by defining an index preserving morphism s: Br(<(K(X))over cap>)` --> Br(K(X))` which splits res : Br(K (X)) --> Br(<(K(X))over cap>), where <(K(X))over cap> is the completion of K (X) at the special fiber, and using it to lift indecomposable and noncrossed product division algebras over <(K(X))over cap>. (C) 2010 Elsevier Inc. All rights reserved.

NONSTATIONARY MIXING AND THE UNIQUE ERGODICITY OF ADIC TRANSFORMATIONS

We define topological and measure-theoretic mixing for nonstationary dynamical systems and prove that for a nonstationary subshift of finite type, topological mixing implies the minimality of any adic transformation defined on the edge space, while if the Parry measure sequence is mixing, the adic transformation is uniquely ergodic. We also show this measure theoretic mixing is equivalent to weak ergodicity of the edge matrices in the sense of inhomogeneous Markov chain theory.

p-adic L functions and trivial zeroes

The following is adapted from the notes for the lecture. It announces results and conjectures about values of the p-adic L function of the symmetric square of an elliptic curve.

Retorică adică învăţătura şi întocmirea frumoasei cuvântări acum întăiu izbodită pe limba romăneaseă...

T.P. and text in the Cyrillic alphabet.

On Selmer groups and factoring p-adic L-functions

Thesis (Ph.D.)--University of Washington, 2016-06

Improved Cryptoanalysis of the Self-shrinking P-adic Cryptographic Generator

The Self-shrinking p-adic cryptographic generator (SSPCG) is a fast software stream cipher. Improved cryptoanalysis of the SSPCG is introduced. This cryptoanalysis makes more precise the length of the period of the generator. The linear complexity and the cryptography resistance against most recently used attacks are invesigated. Then we discuss how such attacks can be avoided. The results show that the sequence generated by a SSPCG has a large period, large linear complexity and is stable against the cryptographic attacks. This gives the reason to consider the SSPSG as suitable for critical cryptographic applications in stream cipher encryption algorithms.

Pseudo-randomness of round-off errors in discretized linear maps on the plane

We analyze the sequences of round-off errors of the orbits of a discretized planar rotation, from a probabilistic angle. It was shown [Bosio & Vivaldi, 2000] that for a dense set of parameters, the discretized map can be embedded into an expanding p-adic dynamical system, which serves as a source of deterministic randomness. For each parameter value, these systems can generate infinitely many distinct pseudo-random sequences over a finite alphabet, whose average period is conjectured to grow exponentially with the bit-length of the initial condition (the seed). We study some properties of these symbolic sequences, deriving a central limit theorem for the deviations between round-off and exact orbits, and obtain bounds concerning repetitions of words. We also explore some asymptotic problems computationally, verifying, among other things, that the occurrence of words of a given length is consistent with that of an abstract Bernoulli sequence.

Tree automorphisms and quasi-isometries of Thompson's group F

We prove that automorphisms of the infinite binary rooted tree T2 do not yield quasi-isometries of Thompson's group F, except for the map which reverses orientation on the unit interval, a natural outer automorphism of F. This map, together with the identity map, forms a subgroup of Aut(T2) consisting of 2-adic automorphisms, following standard terminology used in the study of branch groups. However, for more general p, we show that the analgous groups of p-adic tree automorphisms do not give rise to quasiisometries of F(p).

Spaces with Noetherian cohomology

Is the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? This note provides, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens-Venkov Theorem. We consider the cohomology of a space with coefficients in a module, and we compare Noetherianity over the field with p elements, with Noetherianity over the p-adic integers, in the case when the fundamental group is a finite p-group.

Análisis, diseño e implementación de una aplicación Web para el seguimiento del proceso académico haciendo uso de la arquitectura .NET

En este trabajo final de carrera se ha desarrollado una aplicación Web para el seguimiento vía Internet del proceso académico de los alumnos, tanto por ellos mismos como por parte de sus padres. La aplicación se ha implementado usando la arquitectura .NET de Microsoft para el desarrollo y la tecnología ADO para el acceso a datos.

Generating functions for the numbers of Abelian extensions of a local field

The aim of this paper is to give an explicit formula for the num- bers of abelian extensions of a p-adic number field and to study the generating function of these numbers. More precisely, we give the number of abelian ex- tensions with given degree and ramification index, and the number of abelian extensions with given degree of any local field of characteristic zero. Moreover, we give a concrete expression of a generating function for these last numbers

The Brauer group and the second Abel-Jacobi map for 0-cycles on algebraic varieties

This paper focuses on the connection between the Brauer group and the 0-cycles of an algebraic variety. We give an alternative construction of the second l-adic Abel-Jacobi map for such cycles, linked to the algebraic geometry of Severi-Brauer varieties on X. This allows us then to relate this Abel-Jacobi map to the standard pairing between 0-cycles and Brauer groups (see [M], [L]), completing results from [M] in this direction. Second, for surfaces, it allows us to present this map according to the more geometrical approach devised by M. Green in the framework of (arithmetic) mixed Hodge structures (see [G]). Needless to say, this paper owes much to the work of U. Jannsen and, especially, to his recently published older letter [J4] to B. Gross.

Mineralização do carbono e nitrogênio de resíduos aplicados ao solo em campo

A definição das doses de aplicação de resíduos orgânicos de origens agrícola, urbana ou industrial, com vistas a seu aproveitamento agrícola, deve estar fundamentada na taxa de sua mineralização no solo. Neste trabalho, os objetivos foram utilizar e analisar diferentes métodos de estimativa das frações mineralizadas dos estercos de bovinos, suínos e galinhas, bem como do lodo de esgoto e do composto de lixo urbano, em campo, quando incorporados ou dispostos sobre um Latossolo Vermelho-Amarelo distrófico (LVAd). O experimento foi conduzido por um período de 360 dias, sendo feita coleta mensal de amostras do solo/resíduo, em que foram quantificadas as concentrações de carbono facilmente oxidável (COfo), o nitrogênio total, o amônio e o nitrato, possibilitando a estimativa do nitrogênio orgânico (NO). Verificou-se que estimativas das frações mineralizadas em resíduos dispostos superficialmente estão mais sujeitas a erros que as incorporadas, em razão das diferentes proporções resíduo/solo coletadas durante o período de monitoramento. Recomendou-se a obtenção das frações mineralizadas a partir de dados de concentração de COfo no solo/resíduo, tendo em vista que as de Ninorg e, consequentemente, de NO estão sujeitas à forte influência da ocorrência de chuvas, gerando valores pouco confiáveis. As frações mineralizadas de COfo e NO estimadas, considerando-se as adições de material orgânico (COfo(adic) ou NO(adic)), foram, após 120 dias de incubação do resíduo, superiores a 89,3 %, sejam nos resíduos incorporados ou dispostos superficialmente.