Genus bounds for curves with fixed Frobenius eigenvalues
arXiv:1006.0822 · doi:10.1090/S0002-9939-2013-11839-3
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.
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