Special cycles for Shtukas are closed

Abstract

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