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

Fité Naya, FrancescGuitart Morales, Xavier2023-02-132023-11-062022-11-060025-5874https://hdl.handle.net/2445/193536Abstract. 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.21 p.application/pdfeng(c) Springer Verlag, 2022Varietats abelianesGrups discontinusGeometria algebraicaTeoria de nombresAbelian varietiesDiscontinuous groupsAlgebraic geometryNumber theoryTate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of $\mathrm{GL}_2$-typeinfo:eu-repo/semantics/article7174042023-02-13info:eu-repo/semantics/openAccess