Fox-Neuwirth-Fuks cells, quantum shuffle algebras, and Malle’s conjecture for function fields

Jordan S. Ellenberg; Tri Thang Tran; Craig Westerland

Fox-Neuwirth-Fuks cells, quantum shuffle algebras, and Malle’s conjecture for function fields

Jordan S. Ellenberg, Tri Thang Tran, Craig Westerland

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The purpose of this paper is to prove the upper bound in Malle’s conjecture on the distribution of finite extensions of F_q(t) with specified Galois group. As in [EVW16], our result is based upon computations of the homology of braid groups with certain (exponential) coefficients. However, the approach in this paper is new, relying on a connection between the cohomology of Hurwitz spaces and the cohomology of quantum shuffle algebras.

MSC Codes 11G20, 11S20, 55R80, 20J06, 14H10, 16T05

Original language	English (US)
Journal	Unknown Journal
State	Published - Jan 17 2017

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title = "Fox-Neuwirth-Fuks cells, quantum shuffle algebras, and Malle{\textquoteright}s conjecture for function fields",

abstract = "The purpose of this paper is to prove the upper bound in Malle{\textquoteright}s conjecture on the distribution of finite extensions of Fq(t) with specified Galois group. As in [EVW16], our result is based upon computations of the homology of braid groups with certain (exponential) coefficients. However, the approach in this paper is new, relying on a connection between the cohomology of Hurwitz spaces and the cohomology of quantum shuffle algebras.MSC Codes 11G20, 11S20, 55R80, 20J06, 14H10, 16T05",

author = "Ellenberg, {Jordan S.} and Tran, {Tri Thang} and Craig Westerland",

year = "2017",

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language = "English (US)",

journal = "Journal of Fluid Mechanics",

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AU - Ellenberg, Jordan S.

AU - Tran, Tri Thang

AU - Westerland, Craig

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Y1 - 2017/1/17

N2 - The purpose of this paper is to prove the upper bound in Malle’s conjecture on the distribution of finite extensions of Fq(t) with specified Galois group. As in [EVW16], our result is based upon computations of the homology of braid groups with certain (exponential) coefficients. However, the approach in this paper is new, relying on a connection between the cohomology of Hurwitz spaces and the cohomology of quantum shuffle algebras.MSC Codes 11G20, 11S20, 55R80, 20J06, 14H10, 16T05

AB - The purpose of this paper is to prove the upper bound in Malle’s conjecture on the distribution of finite extensions of Fq(t) with specified Galois group. As in [EVW16], our result is based upon computations of the homology of braid groups with certain (exponential) coefficients. However, the approach in this paper is new, relying on a connection between the cohomology of Hurwitz spaces and the cohomology of quantum shuffle algebras.MSC Codes 11G20, 11S20, 55R80, 20J06, 14H10, 16T05

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JF - Journal of Fluid Mechanics

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