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

DOI10.4007/annals.2016.183.3.1zbMath1342.14055arXiv0912.0325OpenAlexW2962706854WikidataQ104088647 ScholiaQ104088647MaRDI QIDQ291013

Jordan S. Ellenberg, Akshay Venkatesh, Craig Westerland

Publication date: 6 June 2016

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.0325

zbMATH Keywords

Hurwitz spaceclass grouphomological stabilityarithmetic statistics

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Families, moduli of curves (algebraic) (14H10) Curves over finite and local fields (11G20) Coverings of curves, fundamental group (14H30) Positive characteristic ground fields in algebraic geometry (14G17)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Cohen-Lenstra heuristic and roots of unity
• Stabilization for mapping class groups of 3-manifolds
• On the 4-rank of class groups of quadratic number fields
• The integral monodromy of hyperelliptic and trielliptic curves
• Stability of the homology of the mapping class groups of orientable surfaces
• Topology of the complement of real hyperplanes in \({\mathbb C}^ N\)
• The topology of spaces of rational functions
• La conjecture de Weil. II
• Finiteness theorems in geometric classfield theory. (With an appendix by Kenneth A. Ribet)
• The inverse Galois problem and rational points on moduli spaces
• The homology of iterated loop spaces
• The cohomology ring of the colored braid group
• La conjecture de Weil. I
• Random matrices, the Cohen-Lenstra heuristics, and roots of unity
• Big symplectic or orthogonal monodromy modulo \(\ell\)
• The number of extensions of a number field with fixed degree and bounded discriminant
• Local triviality of the restriction map for embeddings
• Séminaire de géométrie algébrique du Bois-Marie 1967--1969. Groupes de monodromie en géométrie algébrique (SGA 7 II) par P. Deligne et N. Katz. Exposés X à XXII
• \(S\)-units and \(S\)-class group in algebraic function fields
• Theory of braids
• Homological stability for mapping class groups of surfaces
• Some Remarks on Cohen-Lenstra Heuristics
• Function fields with class number indivisible by a prime l
• The projectivity of the moduli space of stable curves, II: The stacks $M_{g,n}$
• Class Number Divisibility in Real Quadratic Function Fields
• Indivisibility of class numbers of imaginary quadratic function fields
• Density of discriminants of cubic extensions.
• Stable real cohomology of arithmetic groups
• Mapping Class Groups and Moduli Spaces of Curves
• Twisted Bundles and Admissible Covers
• The Arithmetic of Polynomials in a Galois Field
• Les Schémas de Modules de Courbes Elliptiques
• STABILITY THEOREMS FOR SPACES OF RATIONAL CURVES

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