Supersingular genus-two curves over fields of characteristic three
Number Theory
2010-01-23 v1 Algebraic Geometry
Abstract
Let C be a supersingular genus-2 curve over an algebraically closed field of characteristic 3. We show that if C is not isomorphic to the curve y^2 = x^5 + 1 then up to isomorphism there are exactly 20 degree-3 maps phi from C to the elliptic curve E with j-invariant 0. We study the coarse moduli space of triples (C,E,phi), paying particular attention to questions of rationality. The results we obtain allow us to determine, for every finite field k of characteristic 3, the polynomials that occur as Weil polynomials of supersingular genus-2 curves over k.
Keywords
Cite
@article{arxiv.math/0604413,
title = {Supersingular genus-two curves over fields of characteristic three},
author = {Everett W. Howe},
journal= {arXiv preprint arXiv:math/0604413},
year = {2010}
}
Comments
20 pages, LaTeX