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This would be a vague question, but I still want to ask here. Do you have any recommended book on complex multiplicaton. I know only 2 books: Shimura's book Abelian Varieties with Complex Multiplication and Modular Functions and Lang's book Complex Multiplication. Shimura's book used old-language (published in 1961), and I feel it would be nice to read this book when I have already learned complex multiplication. (But it would be great to know if there is something treated only or treated well in this book compared to other resource). There is also Milne's note.

So other than these, do you have recommended books or notes?

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The elliptic curve case is treated very well in Silverman II, and the link with class field theory (still in the elliptic curve case) is explained well by Serre in Cassels-Froehlich. For me, learning the elliptic curve theory first was a good gateway into the general theory (which I learnt from Shimura's book). –  Kevin Buzzard Jun 12 '12 at 0:24
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As well as Milne's notes, there is this nice set of notes by Laurent Fargues: www-irma.u-strasbg.fr/~fargues/Motifs_abeliens.pdf Regards, –  Emerton Jun 12 '12 at 2:05
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Can we close this so it doesn't keep popping up to the front page? It seems like it was answered in the comments... –  Steven Gubkin Jul 24 '12 at 17:13

1 Answer 1

(i) "Complex Multiplication", Schertz, Cambridge University Press (2010)

or

(ii) Chapter 2 of "Advanced Topics in the Arithmetic of Elliptic Curves", Silverman
(Springer).

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