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.

arXiv commentAdded 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

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Cited by in corpus (10)

• Virtual fundamental classes of derived stacks I
• The motivic Satake equivalence
• Tate motives on Witt vector affine flag varieties
• On the Nori and Hodge realisations of Voevodsky motives
• The Nisnevich Motive of an Algebraic Stack
• The geometric Satake equivalence for integral motives
• Néron blowups and low-degree cohomological applications
• Mixed Hodge modules on stacks
• $T$-equivariant motives of flag varieties
• Cellular pavings of fibers of convolution morphisms