The intersection motive of the moduli stack of shtukas

Abstract

For a split reductive group G over a finite field, we show that the intersection (cohomology) motive of the moduli stack of iterated G-shtukas with bounded modification and level structure is defined independently of the standard conjectures on motivic t-structures on triangulated categories of motives. This is in accordance with general expectations on the independence of l in the Langlands correspondence for function fields.

Added a comparison with equivariant higher Chow groups, further minor edits. Final version, to appear in Forum of Mathematics Sigma. The former section 6 on Motives on Witt vector affine flag varieties has been removed and will appear elsewhere