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
Outline and lecture topics to be announced.
Prerequisites
Chapter III of Arithmetic of Elliptic Curves by Silverman. Some familiarity with varieties would be helpful.
Problem Sets & Materials
Problem sets and lecture notes will be posted here.