Non-supersingular Hyperelliptic jacobians
Algebraic Geometry
2016-09-07 v2 Number Theory
Abstract
In his previous papers the author proved that in characteristic different from 2 the jacobian J(C) of a hyperelliptic curve C: y^2=f(x) has only trivial endomorphisms over an algebraic closure K_a of the ground field K if the Galois group of the irreducible polynomial f(x) in K[x] is either the full symmetric group S_n or the alternating group A_n. Here n > 8 is the degree of f. The goal of this paper is to extend this result to the case when either n=7,8 or n=5,6 and char(K)>3.
Cite
@article{arxiv.math/0311137,
title = {Non-supersingular Hyperelliptic jacobians},
author = {Yuri G. Zarhin},
journal= {arXiv preprint arXiv:math/0311137},
year = {2016}
}
Comments
Minor inaccuracies/typos were corrected. The paper will appear in Bull. Soc. Math. France