Hyperelliptic jacobians without complex multiplication in positive characteristic
Abstract
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), 123132).
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2001
 arXiv:
 arXiv:math/0101050
 Bibcode:
 2001math......1050Z
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory;
 14H40;
 14K05;
 11G30;
 11G10
 EPrint:
 LaTeX2e, 6 pages