Truncated projective spaces, Brown–Gitler spectra and indecomposable A(1)-modules
Contribuinte(s) |
Laboratoire Angevin de REcherche en MAthématiques (LAREMA) ; Centre National de la Recherche Scientifique (CNRS) - Université d'Angers (UA) |
---|---|
Data(s) |
2015
|
Resumo |
<p>MSC 19L41; 55S10.</p> International audience <p>A structure theorem for bounded-below modules over the subalgebra A(1)A(1) of the mod-2 Steenrod algebra generated by Sq1, Sq2 is proved; this is applied to prove a classification theorem for a family of indecomposable A(1)A(1)-modules. The action of the A(1)A(1)-Picard group on this family is described, as is the behaviour of duality.</p><p>The cohomology of dual Brown–Gitler spectra is identified within this family and the relation with members of the A(1)A(1)-Picard group is made explicit. Similarly, the cohomology of truncated projective spaces is considered within this classification; this leads to a conceptual understanding of various results within the literature. In particular, a unified approach to Ext-groups relevant to Adams spectral sequence calculations is obtained, englobing earlier results of Davis (for truncated projective spaces) and recent work of Pearson (for Brown–Gitler spectrum).</p> |
Identificador |
hal-01392103 https://hal.archives-ouvertes.fr/hal-01392103 DOI : 10.1016/j.topol.2014.12.023 OKINA : ua12549 |
Idioma(s) |
en |
Publicador |
HAL CCSD |
Relação |
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.topol.2014.12.023 |
Fonte |
ISSN: 1879-3207 Topology and its Applications https://hal.archives-ouvertes.fr/hal-01392103 Topology and its Applications, 2015, 183, pp.45-85. <10.1016/j.topol.2014.12.023> |
Palavras-Chave | #Brown–Gitler spectra #indecomposable module #Steenrod algebra #truncated projective space #[MATH] Mathematics [math] |
Tipo |
info:eu-repo/semantics/article Journal articles |