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2022-11-06

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/193536

Tate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of $\mathrm{GL}_2$-type

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https://doi.org/10.1007/s00209-021-02895-4

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.

Subject

Varietats abelianes, Grups discontinus, Geometria algebraica, Teoria de nombres

Subject (English)

Abelian varieties, Discontinuous groups, Algebraic geometry, Number theory

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

FITÉ NAYA, Francesc and GUITART MORALES, Xavier. Tate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of $\mathrm{GL}_2$-type. Mathematische Zeitschrift. 2022. Vol. 300, num. 3, pags. 2975-2995. ISSN 0025-5874. [consulted: 16 of August of 2026]. Available at: https://hdl.handle.net/2445/193536

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