Abelian varieties without homotheties

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dc.creatorZarhin, Yuri G.
dc.date2006-06-19
dc.date2006-10-16
dc.date.accessioned2026-07-07T07:17:24Z
dc.date.available2026-07-07T07:17:24Z
dc.descriptionA 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 $p$.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/math/0606422
dc.identifierhttp://arxiv.org/abs/math/0606422
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/113928
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject11G10; 14G25
dc.titleAbelian varieties without homotheties
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