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, a positive fraction of quadratic extensions of Fq(t) have the ℓ-part of their class group isomorphic to A.
Original language | English (US) |
---|---|
Pages (from-to) | 729-786 |
Number of pages | 58 |
Journal | Annals of Mathematics |
Volume | 183 |
Issue number | 3 |
DOIs | |
State | Published - May 1 2016 |
Bibliographical note
Publisher Copyright:© 2016 Department of Mathematics, Princeton University.