An averaging formula for the cohomology of PEL-type Rapoport--Zink spaces

Alexander Bertoloni Meli

Published 2021-03-22Version 1

We prove under certain assumptions a formula for the cohomology of PEL-type Rapoport--Zink spaces that ``averages'' over the Kottwitz set. Our formula generalizes that of Shin's beyond the EL-type case and is proven by combining Mantovan's formula with descriptions of the cohomology of Shimura and Igusa varieties. We then use this averaging formula to derive a conjectural description of the cohomology of Rapoport--Zink spaces, generalizing our earlier work for EL-type spaces. Along the way, we give a description of the cohomology of Igusa varieties in terms of the Langlands correspondence, generalizing work in Shin's thesis.