Y. Zarhin Title: Abelian varieties without homotheties.

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 for an ordinary elliptic curve over a finite field. We discuss an explicit construction of non-constant absolutely simple ordinary abelian varieties without homotheties over global fields in characteristic p.

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