The leading constant in Malle's conjecture over function fields
Abstract
We prove the analogue of Malle's conjecture for the global function field 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 q points of configuration spaces as a certain Tamagawa volume.
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