2026-04-17T01:36:37Zhttps://recercat.cat/oai/requestoai:recercat.cat:2445/1935362025-12-05T09:58:54Zcom_2072_1057col_2072_478917col_2072_478920
Tate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of $\mathrm{GL}_2$-type
Fité Naya, Francesc
Guitart Morales, Xavier
Varietats abelianes
Grups discontinus
Geometria algebraica
Teoria de nombres
Abelian varieties
Discontinuous groups
Algebraic geometry
Number theory
Abstract. We introduce a tensor decomposition of the $\ell$-adic Tate module of an abelian variety $A_0$ defined over a number field which is geometrically isotypic and potentially of $\mathrm{GL}_2$-type. We use this decomposition as a fundamental tool to describe the Sato-Tate group of $A_0$ and to prove the Sato-Tate conjecture in certain cases.
2023-02-13T17:24:39Z
2023-11-06T06:10:24Z
2022-11-06
2023-02-13T17:24:39Z
info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
Versió postprint del document publicat a: https://doi.org/10.1007/s00209-021-02895-4
Mathematische Zeitschrift, 2022, vol. 300, num. 3, p. 2975-2995
https://doi.org/10.1007/s00209-021-02895-4
(c) Springer Verlag, 2022
info:eu-repo/semantics/openAccess
Springer Verlag
Articles publicats en revistes (Matemàtiques i Informàtica)