Homomorphisms of abelian varieties over finite fields

Abstract

These are notes of my lectures at the summer school "Higher-dimensional geometry over finite fields" in Goettingen, June--July 2007. We present a proof of Tate's theorem on homomorphisms of abelian varieties over finite fields (including the $\ell =p$ case) that is based on a "quaternion trick". In fact, a a slightly stronger version of those theorems with "finite coefficients" is proven.

arXiv comment23 pages. Several typos have been corrected