On certain unitary group Shimura varieties

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The Local Langlands Correspondence for GLn over p-adic fields (2012, methodology): “This method has been extended to more general Shimura varieties through the work of Mantovan, [19, 20], and Shin, [27], and allows one to give expressions for the trace of arbitrary Hecke correspondences at p on a Shimura variety.”
Geometrization of the local Langlands correspondence: an overview (2016, background): “This is a reinterpretation of Mantovan’s work in [20] in the perfectoid setting where the nearby cycles RΨη̄ are replaced by RπHT∗.”
On the cohomology of certain PEL-type Shimura varieties (2005, methodology): “The machinery developed in [20] enable us to deduce from the existence of a system of morphisms with these property the existence of a spectral sequence of representations of the Weil group computing the cohomology with compact supports of the strata X̄ Up(0) in terms of the cohomology with compact ”