Point Counting on Igusa Varieties for function fields

Paul Hamacher, Wansu Kim

Published 2022-08-01Version 1

Igusa varieties over the special fibre of Shimura varieties have demonstrated many applications to the Langlands program via Mantovan's formula and Shin's point counting method. In this paper we study Igusa varieties over the moduli space of global $\Gscr$-shtukas and (under certain conditions) calculate the Hecke action on its cohomology. As part of their construction we prove novel results about local $G$-shtukas in both equal und unequal characteristic and also discuss application of these results to Barsotti-Tate groups and Shimura varieties.