2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61579Let $k$ be a totally real field, and let $A/k$ be an absolutely irreducible, polarized Abelian variety of odd, prime dimension whose endomorphisms are all defined over $k$. Then the only strictly compatible families of abstract, absolutely irreducible representations of $\gal(\ov{k}/k)$ coming from $A$ are tensor products of Tate twists of symmetric powers of two-dimensional $λ$-adic representations plus field automorphisms. The main ingredients of the proofs are the work of Borel and Tits on the `abstract' homomorphisms of almost simple algebraic groups, plus the work of Shimura on the fields of moduli of Abelian varieties.Revision, with a new sectionNumber TheoryAlgebraic GeometryPrimary 11G5, 11G10; Secondary 11G15text