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.
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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 -