On finiteness of endomorphism rings of abelian varieties

Details On finiteness of endomorphism rings of abelian varieties On finiteness of endomorphism rings of abelian varieties

2009-04-30

arxiv.org/abs/0905.0019v4

Mathematics

Number Theory

Revised version, 16 pages

Scientific paper

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 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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