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

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arxiv 1701.04541 v2 pith:MVEQPJCZ submitted 2017-01-17 math.NT math.AGmath.ATmath.QA

Jordan S. Ellenberg , TriThang Tran , Craig Westerland This is my paper · ORCID
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keywords algebrascohomologyconjecturemallequantumshuffleapproachbound
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abstract

The purpose of this paper is to prove the upper bound in Malle's conjecture on the distribution of finite extensions of $\mathbb{F}_q(t)$ with specified Galois group. As in previous work of Ellenberg-Venkatesh-Westerland, 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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Homological stability and weak approximation

    math.AG 2025-09 conditional novelty 7.0 of 10

    Homological stability holds for jet-constrained spaces of sections of projective bundles, conic bundles, and quadric surface bundles over a curve.

  2. Representation stability for ordered Hurwitz spaces

    math.AT 2025-09 conditional novelty 7.0 of 10

    The homology groups of ordered Hurwitz spaces, seen as representations of symmetric groups, have stable multiplicities in a range that grows linearly with homological degree.

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