Abelian varieties without homotheties

• Autores: Yuri G. Zarhin
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 14, Nº 1, 2007, págs. 157-164
• Idioma: inglés
• DOI: 10.4310/mrl.2007.v14.n1.a13
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• Resumen

  • A celebrated theorem of Bogomolov asserts that the $\ell$-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 $p$.