Genus bounds for curves with fixed Frobenius eigenvalues
Number Theory
2020-01-16 v2 Algebraic Geometry
Abstract
For every finite collection C of abelian varieties over F_q, we produce an explicit upper bound on the genus of curves over F_q whose Jacobians are isogenous to a product of powers of elements of C.
Cite
@article{arxiv.1006.0822,
title = {Genus bounds for curves with fixed Frobenius eigenvalues},
author = {Noam D. Elkies and Everett W. Howe and Christophe Ritzenthaler},
journal= {arXiv preprint arXiv:1006.0822},
year = {2020}
}
Comments
14 pages. The new version includes new references to papers with related results; also, the main result has been greatly improved, thanks to an argument suggested by Zeev Rudnick and Sergei Konyagin