On finiteness of endomorphism rings of abelian varieties

2009/04/30 by Chia-Fu Yu, Yu, Chia-Fu · 1 citation
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.0905.0019

Revised version, 16 pages

arxiv created 2014/07/02 · arxiv updated 2014/07/03

Abstract

The endomorphism ring End(A) of an abelian variety A is an order in a semi-simple algebra over Q. The co-index of End(A) is the index to a maximal order containing it. We show that for abelian varieties of fixed dimension over any algebraically closed field of characteristic p>0, the p-exponents of the co-indices of their endomorphism rings are bounded. We also give a few applications to this finiteness result.

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