This article is in Cornell-Silverman.

This article gives proofs of the basic properties of Jacobian varieties along with a constructive proof that the Jacobian exists.

Here is a 9 MB scan of the article in PDF format.

There are three articles on abelian varieties; the first by Rosen is on the analytic theory, while the other two by Milne are on the geometric theory in arbitrary characteristics and on Jacobian varieties, respectively. These are the three main approaches to the theory of abelian varieties, and to have all three represented in one place is very pleasant. For example, at the elementary level, the reader can compare the proof that a connected compact complex Lie group is commutative, in Rosen's article, with the proof that a complete group variety is commutative, in the article "Abelian varieties" by Milne. (Note that Section 16 describes Zarkhin's trick, which is used in Faltings' paper.) |