Ordinary Primes for Abelian Surfaces

2015/06/15 by William F. Sawin, Sawin, William F. · 2 citations
Mathematics · #11G10 #11R45 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G10 #msc:11R45

paper · pdf · doi:10.48550/arxiv.1506.04784

4 pages - added references

arxiv created 2015/09/27 · arxiv updated 2015/09/29

Abstract

We compute the density of the set of ordinary primes of an abelian surface over a number field in terms of the l-adic monodromy group. Using the classification of l-adic monodromy groups of abelian surfaces by Fite, Kedlaya, Rotger, and Sutherland, we show the density is 1, 1/2, or 1/4.

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• Positive density of primes of ordinary reduction for abelian varieties of simple signature
• Zero-cycles on quasi-projective surfaces over p-adic fields

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