Homomorphisms of abelian varieties

Abstract

We discuss Galois properties of points of prime order on an abelian variety that imply the simplicity of its endomorphism algebra. Applications to hyperelliptic jacobians are given. In particular, we improve some of our earlier results.

23 pages, to appear in the Proceedings of ``Arithmetic, Geometry and Coding Theory - 9" conference (Luminy, May 2003)