Jacobian Varieties --- J.S. Milne   Top
Expository Notes
A Primer of Commutative Algebra
Motives---Grothendieck's Dream
What is a Shimura Variety?
Introduction to Shimura Varieties
Shimura Varieties and Moduli
Tannakian Categories
The Work of Tate
Errata

Abstract

This the original TeX file for my article Jacobian Varieties, published as Chapter VII of Arithmetic geometry (Storrs, Conn., 1984), 167--212, Springer, New York, 1986. The table of contents has been restored, some corrections and minor improvements to the exposition have been made, and an index has been added. The numbering is unchanged.

The article contains a detailed treatment of Jacobian varieties. Sections 2, 5, and 6 prove the basic properties of Jacobian varieties starting from the definition in Section 1, while the construction of the Jacobian is carried out in Sections 3 and 4. The remaining sections are largely independent of one another.

Contents

  1. Definitions
  2. The canonical maps from C to its Jacobian variety
  3. The symmetric powers of a curve
  4. The construction of the Jacobian variety
  5. The canonical maps from the symmetric powers of C to its Jacobian variety
  6. The Jacobian variety as Albanese variety; autoduality
  7. Weil's construction of the Jacobian variety
  8. Generalizations
  9. Obtaining coverings of curve from its Jacobian
  10. Abelian varieties are quotients of Jacobian varieties
  11. The zeta function of curve
  12. Torelli's theorem: statement and applications
  13. Torelli's theorem: the proof
  14. Bibliographic notes for "Abelian Varieties" and "Jacobian Varieties"

pdf (first posted 12.08.12, 43 pages).