Homomorphisms of abelian varieties over finite fields

Details Homomorphisms of abelian varieties over finite fields Homomorphisms of abelian varieties over finite fields

2007-11-10

arxiv.org/abs/0711.1615v3

Mathematics

Algebraic Geometry

23 pages

Scientific paper

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.

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