Tate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of GL₂-type

2019/09/25 by Fité, Francesc, Guitart, Xavier
#11G10 #11G40 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1909.11712

Abstract

We introduce a tensor decomposition of the ℓ-adic Tate module of an abelian variety A₀ defined over a number field which is geometrically isotypic. If A₀ is potentially of \GL₂-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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