Non-supersingular Hyperelliptic jacobians

2003/11/09 by Zarhin, Yuri G.
#14H40 #14K05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.math/0311137

Abstract

In his previous papers the author proved that in characteristic different from 2 the jacobian J(C) of a hyperelliptic curve C: y²=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.

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