Non-isogenous superelliptic jacobians
Number Theory
2007-05-23 v7 Algebraic Geometry
Abstract
In his previous papers (J. reine angew. Math. 544 (2002), 91--110; math.AG/0103203) the author introduced a certain explicit construction of superelliptic jacobians, whose endomorphism ring is the ring of integers in the th cyclotomic field. (Here is an odd prime.) In the present paper we discuss when these jacobians are mutually non-isogenous. (The case of hyperelliptic jacobians was treated in author's e-print math.NT/0301173 .)
Cite
@article{arxiv.math/0303001,
title = {Non-isogenous superelliptic jacobians},
author = {Yuri G. Zarhin},
journal= {arXiv preprint arXiv:math/0303001},
year = {2007}
}
Comments
LaTeX2e, 16 pages. We extend the main result to a broader class of superelliptic jacobians related to polynomials with doubly transitive Galois groups