Hyperelliptic jacobians without complex multiplication in positive characteristic

Details Hyperelliptic jacobians without complex multiplication in positive characteristic Hyperelliptic jacobians without complex multiplication in positive characteristic

2001-01-06

arxiv.org/abs/math/0101050v1

Mathematics

Algebraic Geometry

LaTeX2e, 6 pages

Scientific paper

We prove that in odd characteristic the jacobian of a hyperelliptic curve
$y^2=f(x)$ has no nontrivial endomorphisms over an algebraic closure of the
ground field if the Galois group of the polynomial $f$ of even degree is ``very
big". The case of characteristic zero was previously treated by the author
(Math. Res. Letters 7(2000), 123--132).

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