English

Homomorphisms of abelian varieties over finite fields

Algebraic Geometry 2020-10-16 v5 Number Theory

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 =p\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.

Keywords

Cite

@article{arxiv.0711.1615,
  title  = {Homomorphisms of abelian varieties over finite fields},
  author = {Yuri G. Zarhin},
  journal= {arXiv preprint arXiv:0711.1615},
  year   = {2020}
}

Comments

23 pages. Several typos have been corrected

R2 v1 2026-06-21T09:42:11.654Z