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 language||English (US)|
|State||Published - Jan 17 2017|