Special cycles for Shtukas are closed

In this paper, we give a different proof of a theorem of Paul Breutmann: for a Bruhat–Tits group scheme $\mathcal{H}$ over a smooth projective curve $X$ and a closed embedding into another smooth affine group scheme $\mathcal{G}$, the induced map on the moduli of Shtukas $\operatorname{Sht}^r_{\mathcal{H}} \to \operatorname{Sht}^r_{\mathcal{G}}$ is schematic, finite and unramified. This result enables one to define special cycles on the moduli stack of Shtukas.

Keywords

Shtukas, special cycles

2010 Mathematics Subject Classification

Primary 14F35. Secondary 11F55.

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The author was partially supported by the Simons Investigatorship and the Packard Fellowship.

Received 3 December 2021

Received revised 5 March 2022

Accepted 13 March 2022

Published 12 January 2023