Local-global compatibility of mod $p$ Langlands program for certain Shimura varieties
Number Theory
2022-09-19 v4
Abstract
We generalize the local-global compatibility result in arXiv:1506.04022 to higher dimensional cases, by examining the relation between Scholze's functor and cohomology of Kottwitz-Harris-Taylor type Shimura varieties. Along the way we prove a cuspidality criterion from type theory. We also deal with compatibility for torsion classes in the case of semisimple mod Galois representations with distinct irreducible components under certain flatness hypotheses.
Cite
@article{arxiv.2106.10674,
title = {Local-global compatibility of mod $p$ Langlands program for certain Shimura varieties},
author = {Kegang Liu},
journal= {arXiv preprint arXiv:2106.10674},
year = {2022}
}
Comments
final version