On the nonexistence of certain curves of genus two
Number Theory
2007-05-23 v1 Algebraic Geometry
Abstract
We prove that if q is a power of an odd prime then there is no genus-2 curve over F_q whose Jacobian has characteristic polynomial of Frobenius equal to x^4 + (2-2q)x^2 + q^2. Our proof uses the Brauer relations in a biquadratic extension of Q to show that every principally polarized abelian surface over F_q with the given characteristic polynomial splits over F_{q^2} as a product of polarized elliptic curves.
Keywords
Cite
@article{arxiv.math/0201311,
title = {On the nonexistence of certain curves of genus two},
author = {Everett W. Howe},
journal= {arXiv preprint arXiv:math/0201311},
year = {2007}
}
Comments
LaTeX, 13 pages