Some Algebraic Properties of Abelian Varieties
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Of necessity, this chapter duplicates to a large extent the corresponding material in Shimura-Taniyama [Sh-T]. We make the transition to the algebraic situation, and we assume that the reader is acquainted with the general theory of abelian varieties. No matter whether the reader picks up the basic properties from my book on the subject (after Weil), Mumford, Shimura (for reduction mod p), or the foundations laid by the Grothendieck school, the reader should end up knowing the same basic theorems. Because of my background, I use the terminology of Weil (generic points when needed), and the language of reduction mod p is that of Shimura. I have recalled with proofs some elementary definitions and properties, and without proof some of the more advanced results in this direction.
KeywordsPrime Ideal Differential Form Local Ring Abelian Variety Algebraic Property
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