Local-global compatibility of mod \(p\) Langlands program for certain Shimura varieties. (English) Zbl 1532.11068
Summary: We generalize the local-global compatibility result in as reported by
P. Scholze [Ann. Sci. Éc. Norm. Supér. (4) 51, No. 4, 811–863 (2018; Zbl 1419.14031)]
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.
MSC:
| 11F80 | Galois representations |
| 11F85 | \(p\)-adic theory, local fields |
| 11S37 | Langlands-Weil conjectures, nonabelian class field theory |
| 14G22 | Rigid analytic geometry |
| 14G35 | Modular and Shimura varieties |
Citations:
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