On some abelian varieties of type IV

2018/03/15 by Steve Thakur, Thakur, Steve · 1 citation
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Advanced Differential Equations and Dynamical Systems #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.1803.05954

Abstract

We study a certain class of simple abelian varieties of type IV (in Albert's classification) over number fields with Mumford-Tate groups of type A. In particular, we show that such abelian varieties have ordinary reduction away from a set of places of Dirichlet density zero, thus confirming a special case of a broader conjecture of Serre's. We also study the splitting types and Newton polygons of the reductions of the abelian varieties of this type with small dimension (nine).

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• Isogenies of certain abelian varieties over finite fields with p-ranks\n zero

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