The intersection motive of the moduli stack of shtukas

TL;DR

This paper proves that the intersection motive of the moduli stack of G-shtukas over finite fields is well-defined independently of standard motivic conjectures, supporting the Langlands program's expectations.

Contribution

It establishes the independence of the intersection motive from standard motivic conjectures for moduli stacks of G-shtukas over finite fields.

Findings

Intersection motive is well-defined independently of motivic t-structure conjectures.

Supports the independence of l in the Langlands correspondence for function fields.

Aligns with theoretical expectations in the Langlands program.

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.