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$\ell$in the Langlands correspondence for function fields.