Measurable motivic sites

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.