# Cornell University, Spring 2016

# Math 7390 -- Abelian Varieties

### Instructor:

Farbod Shokrieh

Office: 436 Malott Hall

Email: farbod@cornell.edu

### Lecture time and place:

Tuesdays and Thursdays 10:10AM - 11:25AM

206 Malott Hall

### Description:

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.

### Prerequisites:

Familiarity with algebraic geometry, especially the language of schemes.

### References:

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,
II,
III) (books)
- Various papers and notes by Mumford, B. Conrad, Bosch and Lütkebohmert.

(Last modified on: January 6, 2016)