Journal
ANNALS OF MATHEMATICS
Volume 183, Issue 3, Pages 729-786Publisher
Princeton Univ, Dept Mathematics
DOI: 10.4007/annals.2016.183.3.1
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Funding
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1406162] Funding Source: National Science Foundation
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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 F-q(t) have the l-part of their class group isomorphic to A.
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