# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1901.04919