Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields

Jordan S. Ellenberg, Akshay Venkatesh, Craig Westerland

Research output: Contribution to journalArticlepeer-review

59 Scopus citations

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 languageEnglish (US)
Pages (from-to)729-786
Number of pages58
JournalAnnals of Mathematics
Volume183
Issue number3
DOIs
StatePublished - May 1 2016

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