Measurable motivic sites

TL;DR

This paper develops a new framework for motivic measures using simplicial motivic sites, enabling the measurement of derived stacks with finiteness conditions, extending previous schemic motivic measures.

Contribution

It introduces relative limit simplicial partial motivic sites and a new notion of motivic measurability, generalizing existing schemic motivic measures to derived stacks.

Findings

Defines relative limit simplicial partial motivic sites.

Establishes a motivic measure for derived stacks.

Generalizes schemic motivic measures to a broader context.

Abstract

We introduce the notion of a relative limit simplicial partial motivic site and a corresponding notion of motivic measurability which specializes to the notion of finite schemic motivic measures of H. Schoutens and the notion of infinite schemic motivic measures of the author. The advantage to working with simplicial motivic sites is that it gives the correct notion of the motivic measure of a derived stacks which have some reasonable finiteness conditions. This work was partially supported by the Chateaubriand Fellowship.