Reductions of abelian varieties of generalized Mumford type

2016/11/19 by Steve Thakur, Thakur, Steve
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1611.06411

openalex publication_date 2016/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the special fibers of a certain class of absolutely simple abelian varieties over number fields with endomorphism rings \bz and possessing l-adic monodromy groups of the least possible rank. We also study the Dirichlet density of the places at which the possible reductions occur and confirm a special case of a broader conjecture for the splitting of reductions of abelian varieties over number fields.

Related

• The splitting of reductions of an abelian variety
• On some abelian varieties of type IV
• On the Mumford-Tate conjecture for abelian varieties with reduction conditions
• Galois representations, Mumford-Tate groups and good reduction of abelian varieties
• Elliptic minuscule pairs and splitting abelian varieties