Cornell University, Spring 2016
Math 7390 -- Abelian Varieties
Office: 436 Malott Hall
Lecture time and place:
Tuesdays and Thursdays 10:10AM - 11:25AM
206 Malott Hall
This is an introductory course on the analytic and algebraic theory of abelian (and jacobian) varieties.
We will start with the classical complex-analytic case to build some intuition. Then we will discuss the general theory over other fields.
More advanced topics could include:
- Degenerating families,
- Non-Archimedean uniformization,
- Heights and metrized line bundles,
- Theta functions,
- Néron Models.
Familiarity with algebraic geometry, especially the language of schemes.
We will not follow any specific books. I will use the following resources while preparing for the lectures:
- Mumford - Abelian Varieties (book, known typos)
- Milne - Abelian Varieties (notes available online)
- Birkenhake, Lange - Complex Abelian Varieties (book)
- Faltings, Chai - Degeneration of Abelian Varieties (book)
- Bosch, Lütkebohmert, Raynaud - Néron Models (book)
- Cornell, Silverman - Arithmetic Geometry (book)
- Mumford - Tata Lectures on Theta (I,
- Various papers and notes by Mumford, B. Conrad, Bosch and Lütkebohmert.
(Last modified on: January 6, 2016)