Abelian varieties without homotheties

2006/06/19 by Yuri G. Zarhin, Zarhin, Yuri G.
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.math/0606422

Abstract

A celebrated theorem of Bogomolov asserts that the ℓ-adic Lie algebra attached to the Galois action on the Tate module of an abelian variety over a number field contains all homotheties. This is not the case in characteristic p: a "counterexample" is provided by an ordinary elliptic curve defined over a finite field. In this note we discuss (and explicitly construct) more interesting examples of "non-constant" absolutely simple abelian varieties (without homotheties) over global fields in characteristic p.

Citations

• Good Reduction of Abelian Varieties

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