Connected Components of Hurwitz Schemes and Malle's Conjecture

函数域上的马勒猜想主导常数

The leading constant in Malle's conjecture over function fields

本文通过Hurwitz空间的稳定同调和Brauer群解释，证明了函数域上马勒猜想的主导常数公式。

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

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.

Hurwitz 空间与反 Galois 理论

Hurwitz spaces and Inverse Galois Theory

本文综述了Hurwitz空间在反 Galois 理论中的五十年研究，重点介绍近期进展，包括大域、紧化、降理论和模塔等半现代发展，以及通过研究组件环重塑Hurwitz空间算术的最新成果。

Hurwitz空间的同调稳定性及其应用

Homological stability for Hurwitz spaces and applications

该研究证明了任意有限rack对应的Hurwitz空间同调的整系数稳定性，计算了有限素数倒置后稳定同调的主导部分，证明了Ellenberg–Venkatesh–Westerland猜想并改进了此前非分裂rack的相关结果，还给出了在多个数论猜想与启发式中的应用。

On Some Families of Integrals Connected to the Hurwitz Zeta Function

Expressions for a family of integrals involving the Hurwitz zeta function are established using standard properties of the Fourier transform.

Hurwitz Number Fields

The canonical covering maps from Hurwitz varieties to configuration varieties are important in algebraic geometry. The scheme-theoretic fiber above a rational point is commonly connected, in which case it is the spectrum of a Hurwitz number field. We study many examples of such maps and their fibers, finding number fields whose existence contradicts standard mass heuristics.