The leading constant in Malle's conjecture over function fields

We prove the analogue of Malle’s conjecture for the global function field ${\text{F}}_q(t)$ with $q$ sufficiently large, including a precise formula for the leading constant. The main ingredients are the recent breakthrough of Landesman–Levy on the stable homology of Hurwitz spaces, a novel interpretation of the Frobenius fixed components of Hurwitz spaces in terms of the Brauer group of the stack $BG$ and an interpretation of the number of ${\text{F}}_q$ points of configuration spaces as a certain Tamagawa volume.