Is there any introduction to abelian varieties of CM type?any reference?Like how to construct a abelian varieties given a CM field E?What is the properites of the Mumford Tate group of the abelian varieties of CM type?
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IIRC I learnt a lot from Katz' papers from the 1970s. Of course the basic construction is the same as the elliptic curve case: you take C^g, quotient out by the lattice coming from E via its g embeddings into C, and then you have to prove that the quotient is an abelian variety, which involves writing down a nondegenerate Riemann form. This isn't hard, but I think I first saw it in one of Katz' papers. OhI should say that before I read Katz I read the section on abelian varieties over C in CornellSilverman (although there will be other references for this stuff). 

