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http://hdl.handle.net/2445/193536
Title: | Tate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of $\mathrm{GL}_2$-type |
Author: | Fité Naya, Francesc Guitart Morales, Xavier |
Keywords: | Varietats abelianes Grups discontinus Geometria algebraica Teoria de nombres Abelian varieties Discontinuous groups Algebraic geometry Number theory |
Issue Date: | 6-Nov-2022 |
Publisher: | Springer Verlag |
Abstract: | 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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1007/s00209-021-02895-4 |
It is part of: | Mathematische Zeitschrift, 2022, vol. 300, num. 3, p. 2975-2995 |
URI: | http://hdl.handle.net/2445/193536 |
Related resource: | https://doi.org/10.1007/s00209-021-02895-4 |
ISSN: | 0025-5874 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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717404.pdf | 397.35 kB | Adobe PDF | View/Open |
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