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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:
It is part of: Mathematische Zeitschrift, 2022, vol. 300, num. 3, p. 2975-2995
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ISSN: 0025-5874
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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