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2 questions with no upvoted or accepted answers
11
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What are the possible bad reductions for an abelian variety of dimension $g$ and a maximal endomorphism ring?
Perhaps the most basic fact about abelian varieties with CM is they have an everywhere potential good reduction (Serre-Tate). On the face of it it might appear that there isn't much more to be added ...
5
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Real field of definition of an abelian variety of CM-type?
Question 0. Can a field of definitions (without automorphisms) of an (almost arbitrary) abelian variety of CM-type, originally defined over ${\mathbb{C}}$,
be chosen to be a totally real number ...