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Media type:
E-Article
Title:
Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields
Contributor:
Ellenberg, Jordan S.;
Venkatesh, Akshay;
Westerland, Craig
imprint:
Department of Mathematics at Princeton University, 2016
Published in:
Annals of Mathematics, 183 (2016) 3, Seite 729-786
Language:
English
ISSN:
0003-486X
Origination:
Footnote:
Description:
<p>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.</p>