Tate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of $\mathrm{GL}_2$-type
Number Theory
2021-11-05 v3
Abstract
We introduce a tensor decomposition of the -adic Tate module of an abelian variety defined over a number field which is geometrically isotypic. If is potentially of -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.
Keywords
Cite
@article{arxiv.1909.11712,
title = {Tate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of $\mathrm{GL}_2$-type},
author = {Francesc Fité and Xavier Guitart},
journal= {arXiv preprint arXiv:1909.11712},
year = {2021}
}
Comments
Minor changes. To appear in Math. Zeit