Bounds for Completely Decomposable Jacobians
Number Theory
2010-07-21 v1
Abstract
A curve over the field of two elements with completely decomposable Jacobian is shown to have at most six rational points and genus at most 26. The bounds are sharp. The previous upper bound for the genus was 145. We also show that a curve over the field of elements with more than rational points has at least one Frobenius angle in the open interval . The proofs make use of the explicit formula method.
Cite
@article{arxiv.1007.3344,
title = {Bounds for Completely Decomposable Jacobians},
author = {Iwan Duursma and Jean-Yves Enjalbert},
journal= {arXiv preprint arXiv:1007.3344},
year = {2010}
}
Comments
9 pages, first appeared in 2002, posted for greater accessibility, with an addendum on X(11) mod 2