Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields
By Jordan S. Ellenberg, Akshay Venkatesh, Craig Westerland. 2009
169 citations recorded by the source corpus.
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 ‘ > 2 be prime and A a nite abelian ‘-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 ‘-part of their class group isomorphic to A.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6b165afea6c8ff466348eb1104169f91113efc14
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The distribution of sandpile groups of random regular graphs (2018, background): “is a sequence of random abelian p-groups such that the surjective V -moments of Xn converge to those of X , then the distribution of Xn converge weakly to the distribution ofX? Ellenberg, Venkatesh andWesterland [11] proved that the answer is affirmative for both questions in the special case when e”