ABELIAN VARIETIES

Gerard van der Geer and Ben Moonen
University of Amsterdam
Korteweg-de Vries Institute for Mathematics
Plantage Muidergracht 24
1018 TV Amsterdam
The Netherlands

E-mail: geer (GvdG) or bmoonen (BM), both at the domain science . uva . nl

We are preparing a textbook about abelian varieties. Preliminary versions of some chapters can be downloaded here. Please note that these chapters may be incomplete and, worse, may contain mistakes. You can freely download this material, but as a compensation we ask that you give us some feedback. Any comments, corrections and suggestions are most welcome!

Title page and preliminaries
Chapter 1: Definition and basic examples
Chapter 2: Line bundles and divisors on abelian varieties
Chapter 3: Basic theory of group schemes
Chapter 4: Quotients by group schemes
Chapter 5: Isogenies
Chapter 6: The Picard scheme of an abelian variety
Chapter 7: Duality
Chapter 8: The theta group of a line bundle
Chapter 9: The cohomology of line bundles
Chapter 10: Tate modules, p-divisible groups, and the fundamental group
Chapter 11: Polarizations and the Weil pairing
Chapter 13: The Fourier transform and the Chow ring
References

Under construction (available in **very preliminary and incomplete** form):

Chapter 12: Endomorphims

To the home page of Gerard van der Geer

To the home page of Ben Moonen