2021/03/22 by Alexander Bertoloni Meli, Meli, Alexander Bertoloni
Mathematics · #11G18 #14G35 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G18 #msc:14G35
paper · pdf · doi:10.48550/arxiv.2103.11538
75 pages, comments welcome
arxiv created 2021/04/13 · arxiv updated 2021/04/14
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.