TY - JOUR

T1 - Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields

AU - Ellenberg, Jordan S.

AU - Venkatesh, Akshay

AU - Westerland, Craig

N1 - Publisher Copyright:
© 2016 Department of Mathematics, Princeton University.

PY - 2016/5/1

Y1 - 2016/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84966318498&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966318498&partnerID=8YFLogxK

U2 - 10.4007/annals.2016.183.3.1

DO - 10.4007/annals.2016.183.3.1

M3 - Article

AN - SCOPUS:84966318498

SN - 0003-486X

VL - 183

SP - 729

EP - 786

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 3

ER -