Pure and Applied Mathematics Quarterly

Volume 18 (2022)

Number 5

Special Issue in honor of Professor Benedict Gross’s 70th birthday

Guest Editors: Zhiwei Yun, Shouwu Zhang, and Wei Zhang

Special cycles for Shtukas are closed

Pages: 2203 – 2220

DOI: https://dx.doi.org/10.4310/PAMQ.2022.v18.n5.a6


Zhiwei Yun (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)


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.


Shtukas, special cycles

2010 Mathematics Subject Classification

Primary 14F35. Secondary 11F55.

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