Fabian Schnelle (University of Münster): Igusa stacks for certain abelian-type Shimura varieties

Igusa stacks are objects of p-adic geometry that are supposed to interpolate Igusa varieties and help to analyze the cohomology of Shimura varieties from the vantage point of the categorical local Langlands correspondence. In this talk, I will discuss the construction of Igusa stacks for certain abelian-type Shimura varieties that naturally arise from a PEL datum and are associated with the Weil restriction of an F-group, for F a totally real number field. For this construction, we leverage the existence of certain hybrid spaces that serve as a bridge between PEL-type and abelian-type Shimura varieties.

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