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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 ...

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 ...

If $f : X\to V$ is a smooth proper map of smooth schemes, what are the global sections of $R^if_{fppf, *}\mu_p$ $R^if_{fppf, *}\mathbb{G}_{\rm m}$ I was reading Milne's book "Arithmetic duality", ...