Geodesic
Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields
Jordan S. Ellenberg1 ; Akshay Venkatesh2 ; Craig Westerland3
1 University of Wisconsin, Madison, WI
2 Stanford University, Stanford, CA
3 University of Minnesota, Minneapolis, MN
Annals of mathematics, Tome 183 (2016) no. 3, pp. 729-786.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 $\ell > 2$ be prime and $A$ a finite abelian $\ell$-group. Then there exists $Q = Q(A)$ such that, for $q$ greater than $Q$, a positive fraction of quadratic extensions of $\mathbb{F}_q(t)$ have the $\ell$-part of their class group isomorphic to $A$.
DOI : 10.4007/annals.2016.183.3.1

Jordan S. Ellenberg 1 ; Akshay Venkatesh 2 ; Craig Westerland 3

1 University of Wisconsin, Madison, WI
2 Stanford University, Stanford, CA
3 University of Minnesota, Minneapolis, MN 
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Jordan S. Ellenberg; Akshay Venkatesh; Craig Westerland. Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields. Annals of mathematics, Tome 183 (2016) no. 3, pp. 729-786. doi : 10.4007/annals.2016.183.3.1. http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.183.3.1/

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