Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields
Number Theory
2015-12-03 v4 Algebraic Topology
Abstract
We prove a homological stabilization theorem for Hurwitz spaces: moduli spaces of branched covers of the complex projective line. This has the following arithmetic consequence: let l>2 be prime and A a finite abelian l-group. Then there exists Q = Q(A) such that, for q greater than Q and not congruent to 1 modulo l, a positive fraction of quadratic extensions of F_q(t) have the l-part of their class group isomorphic to A.
Cite
@article{arxiv.0912.0325,
title = {Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields},
author = {Jordan S. Ellenberg and Akshay Venkatesh and Craig Westerland},
journal= {arXiv preprint arXiv:0912.0325},
year = {2015}
}
Comments
47 pages. Minor edits of sections 7-8. Final version; to appear in Annals of Mathematics