A survey around the Hodge, Tate and Mumford-Tate conjectures for abelian varieties

2016/02/26 by Victoria Cantoral‐Farfán, Farfán, Victoria Cantoral
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1602.08354

openalex publication_date 2016/02/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

This survey describe Hodge, Tate and Mumford-Tate conjectures for abelian varieties. After some preliminaries on endomorphism ring, polarization and algebraic cycles, we state the three conjectures and provide a list of know results. Finally, we explain some links between these conjectures.

Citations

• On the \ℓ-adic Galois representations attached to nonsimple abelian\n varieties

Related

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• A note on the Mumford-Tate Conjecture for CM abelian varieties
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• The Tate and Standard Conjectures for Certain Abelian Varieties