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Mar 6, 2017 at 9:59 comment added Francesco Polizzi Maybe not completely, but there are several interesting examples.
Mar 6, 2017 at 9:50 comment added jacob Nope. I found some papers of Oort (say " A construction of an abelian variety with a given endomorphism algebra" eudml.org/doc/89907) which seemed to suggest the problem was tricky. Does that chapter answer the question completely?
Mar 6, 2017 at 9:36 history edited Francesco Polizzi CC BY-SA 3.0
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Mar 6, 2017 at 9:36 comment added Francesco Polizzi Did you look at Chapter 9 of Birkenake-Lange's book Complex Abelian Varieties? Its title is Moduli spaces of abelian varieties with endomorphism structure.
Mar 6, 2017 at 9:30 history asked jacob CC BY-SA 3.0