Fox-Neuwirth-Fuks cells, quantum shuffle algebras, and Malle's conjecture for function fields
Number Theory
2023-03-07 v2 Algebraic Geometry
Algebraic Topology
Quantum Algebra
Abstract
The purpose of this paper is to prove the upper bound in Malle's conjecture on the distribution of finite extensions of 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.
Keywords
Cite
@article{arxiv.1701.04541,
title = {Fox-Neuwirth-Fuks cells, quantum shuffle algebras, and Malle's conjecture for function fields},
author = {Jordan S. Ellenberg and TriThang Tran and Craig Westerland},
journal= {arXiv preprint arXiv:1701.04541},
year = {2023}
}
Comments
81 pages. Substantially revised. The most significant change is a new approach to controlling the homological algebra of connected graded algebras in terms of their Koszul complex