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

Jordan S. Ellenberg, Tri Thang Tran, Craig Westerland

Research output: Contribution to journalArticlepeer-review

Abstract

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

Original languageEnglish (US)
JournalUnknown Journal
StatePublished - Jan 17 2017

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