Cornell University, Spring 2016

Math 7390 -- Abelian Varieties

Instructor:

Lecture time and place:

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:

• 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.