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.
Original language | English (US) |
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Pages (from-to) | 157-164 |
Number of pages | 8 |
Journal | Mathematical Research Letters |
Volume | 14 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2007 |
All Science Journal Classification (ASJC) codes
- General Mathematics