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arXiv · 1909.11712

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

Francesc Fité·Xavier Guitart
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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. If $A_0$ is potentially of $\GL_2$-type and defined over a totally real number field, we use this decomposition to describe its Sato--Tate group and to prove the Sato--Tate conjecture in certain cases.

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Francesc Fité, Xavier Guitart. 2019-09-25. Tate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of $\mathrm{GL}_2$-type. https://arxiv.org/abs/1909.11712

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