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arXiv · 2510.25437

Truncations and the Motive of the Stack of Local $G$-Shtukas

Can Yaylali
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Abstract

We compute the rational motive of the stack of local $G$-shtukas, for a split reductive group $G$, representing compactly supported cohomology in terms of the motive of the stack of $G$-zips. This result makes explicit use of the truncated version of local $G$-shtukas established by Viehmann-Wedhorn and the theoretical background on the $*$- and $!$-adjunction for pro-systems of algebraic objects established by the author.

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Can Yaylali. 2025-10-29. Truncations and the Motive of the Stack of Local $G$-Shtukas. https://arxiv.org/abs/2510.25437

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