`Abstract' homomorphisms of l-adic Galois groups and Abelian varieties

2001/06/03 by Siman Wong, Wong, Siman
Mathematics · #11G10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Primary 11G5 #Secondary 11G15 #advanced mathematical theories #math.AG #math.NT #msc:11G10 #msc:11G15 #msc:11G5

paper · pdf · doi:10.48550/arxiv.math/0106016

Revision, with a new section

openalex publication_date 2001/06/03 · arxiv created 2001/07/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let 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(\ovk/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.

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