Moments in families of L-functions over function fields

1. Question by Aaron Landesman on racks

Is there a common generalization of Malle’s conjecture and the Davis-Schlank conjecture that gives asymptotics for c extensions extensions for a rack? The relevant homological stability result is per component is known due to a result of Landesman-Levy over 𝔽⎯⎯⎯q. Namely, there is a Hurwitz space Hurcn parameterizing rack covers “branched over a degree n divisor. See Definition 2.2.2 of the paper by Landesman-Levy on ”Homological stability for Hurwitz spaces and Applications.“ Part of this question is to explain what the relevant variety over 𝔽q. The challenge is to descend this to the same 𝔽q for all n. Mark Shusterman has some first thoughts on how one might define this. One of the interesting questions would be to understand the relevant number of components. What are arithmetic consequences of objects not coming from Hurwitz spaces. Does this come with a moduli interpretation?