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arXiv · 2106.10674

Local-global compatibility of mod $p$ Langlands program for certain Shimura varieties

Kegang Liu
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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 $p$ Galois representations with distinct irreducible components under certain flatness hypotheses.

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Kegang Liu. 2021-06-20. Local-global compatibility of mod $p$ Langlands program for certain Shimura varieties. https://doi.org/10.1007/s00229-022-01410-1

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