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l-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficients

Research output: Contribution to journalArticlepeer-review

P Hamacher, Wansu Kim

Original languageEnglish
JournalMathematische Annalen
Accepted/In press21 Feb 2019

King's Authors


Let (G; X) be a Shimura datum of Hodge type. Let p be an odd prime
such that GQp splits after a tamely ramified extension and p - j1(Gder)j. Under
some mild additional assumptions that are satisfied if the associated Shimura
variety is proper and GQp is either unramified or residually split, we prove the
generalisation of Mantovan’s formula for the l-adic cohomology of the associated
Shimura variety. On the way we derive some new results about the geometry of the
Newton stratification of the reduction modulo p of the Kisin-Pappas integral model.

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