Motives for shtukas and Shimura varieties

Basic data for this project

Description

The first goal is to calculate the motive of the classifying stack of a reductive group and of the stack of G-zips for a reductive group G defined over a finite field. From this we will build the motive of moduli spaces of local G-shtukas and truncated local G-shtukas, including a generalization to the case of non-constant smooth group schemes G. The third goal is to calculate the motive of the moduli space of truncated G-displays of a fixed type and to apply this to higher Chow groups of Shimura varieties of abelian type.