Course Title
Elliptic curves and abelian varieties over finite fields
Abstract
The lectures will give an introduction to elliptic curves and abelian varieties over finite fields. We will first cover Tate's theorem on endomorphisms and isogenies, the classification of isogeny classes of abelian varieties via Weil polynomials and Honda–Tate theory, and an introduction to finite flat group schemes and \(p\)-divisible groups. The final part of the course will be on the deformation theory of abelian varieties and \(p\)-divisible groups, with a focus on examples.
Lecture Topics
- Tate's theorem on endomorphisms of abelian varieties.
- The Honda–Tate classification.
- CM lifts and rational curves.
- Frobenius semisimplicity via Hecke correspondences.