Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields

Jordan S. Ellenberg, Akshay Venkatesh, Craig Westerland

Type: Article

Publication Date: 2016-04-18

Citations: 108

DOI: https://doi.org/10.4007/annals.2016.183.3.1

Abstract

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.

Locations

arXiv (Cornell University) - View - PDF
Annals of Mathematics - View

Similar Works

Action	Title	Year	Authors
+	Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields	2009	Jordan S. Ellenberg Akshay Venkatesh Craig Westerland
+	Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields, II	2012	Jordan S. Ellenberg Akshay Venkatesh Craig Westerland
+	Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields, II	2012	Jordan S. Ellenberg Akshay Venkatesh Craig Westerland
+	Homological stability for generalized Hurwitz spaces and Selmer groups in quadratic twist families over function fields	2023	Jordan S. Ellenberg Aaron Landesman
+	Polynomial stability of the homology of Hurwitz spaces	2023	Andrea Bianchi Jeremy Miller
+	Moduli spaces of covers and the Hurwitz monodromy group.	1982	M. Fried R. Biggers
+ PDF Chat	Hurwitz moduli varieties parameterizing pointed covers of an algebraic curve with a fixed monodromy group	2024	Vassil Kanev
+	Plant complexes and homological stability for Hurwitz spaces	2016	J. Frederik Tietz
+ PDF Chat	STABILITY THEOREMS FOR SPACES OF RATIONAL CURVES	2001	Charles P. Boyer Jacques Hurtubise R. James Milgram
+	The Geometry of Rings of Components of Hurwitz Spaces	2022	Béranger Seguin
+	Branch Stabilisation for the Components of Hurwitz Moduli Spaces of Galois Covers.	2019	Michael Lönne
+	Cohen-Lenstra heuristics and local conditions.	2017	Melanie Matchett Wood
+ PDF Chat	Cohen-Lenstra heuristics and local conditions	2018	Melanie Matchett Wood
+	Homology of Hurwitz spaces and the Cohen--Lenstra heuristic for function fields (after Ellenberg, Venkatesh, and Westerland)	2019	Oscar Randal‐Williams
+	Polynomial stability of the homology of Hurwitz spaces	2024	Andrea Bianchi Jeremy Miller
+	Hurwitz moduli varieties parameterizing Galois covers of an algebraic curve	2022	Vassil Kanev
+	Homology of Hurwitz spaces and the Cohen--Lenstra heuristic for function fields (after Ellenberg, Venkatesh, and Westerland)	2019	Oscar Randal‐Williams
+ PDF Chat	A geometric approach to the Jacobian Conjecture in ℂ²	1991	Ludwik M. Drużkowski
+ PDF Chat	Branch Stabilisation for the Components of Hurwitz Moduli Spaces of Galois Covers	2020	Michael Lönne
+	Branch Stabilisation for the Components of Hurwitz Moduli Spaces of Galois Covers	2019	Michael Lönne

Works That Cite This (110)

Action	Title	Year	Authors
+	The distribution of sandpile groups of random regular graphs	2020	András Mészáros
+ PDF Chat	Singularities and vanishing cycles in number theory over function fields	2020	Will Sawin
+	The distribution of sandpile groups of random graphs	2016	Melanie Matchett Wood
+	Deloopings of Hurwitz spaces	2024	Andrea Bianchi
+	An epsilon of room, I : real analysis : pages from year three of a mathematical blog	2010	Terence Tao
+ PDF Chat	Random integral matrices and the Cohen-Lenstra heuristics	2019	Melanie Matchett Wood
+ PDF Chat	LONELY RUNNERS IN FUNCTION FIELDS	2019	Sam Chow Luka Rimanić
+ PDF Chat	Coloring invariants of knots and links are often intractable	2021	Greg Kuperberg Eric Samperton
+	Cohen-Lenstra distributions via random matrices over complete discrete valuation rings with finite residue fields	2018	Gilyoung Cheong Yifeng Huang
+	The homotopy types of free racks and quandles	2021	Tyler Lawson Markus Szymik

Works Cited by This (52)

Action	Title	Year	Authors
+	Finiteness Theorems in Geometric Classfield Theory	2000	Nicholas M. Katz Serge Lang Kenneth A. Ribet
+	Finite generation of the groups Ki of rings of algebraic integers	1973	Daniel Quillen
+ PDF Chat	Mapping class groups and moduli spaces of curves	1997	Richard Hain Eduard Looijenga
+	On the distribution of divisor class groups of curves over a finite field	1989	Eduardo Friedman Lawrence C. Washington
+	Commutative Ring Theory	1987	H. Matsumura
+ PDF Chat	Groupes de Monodromie en Géométrie Algébrique	1973	P. Deligne Nicholas M. Katz Nicholas M. Katz
+ PDF Chat	Homology of iterated loop spaces	2001	В. А. Смирнов
+	Stable Real Cohomology of Arithmetic Groups II	1981	Armand Borel
+	Etale Cohomology and the Weil Conjecture	1988	Eberhard Freitag Reinhardt Kiehl
+	Étude heuristique des groupes de classes des corps de nombres.	1990	Henri Cohen Jacques Martinet