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Talk 8: Cohomology of Shimura varieties via the Hodge-Tate period map

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Peter Scholze
Fri, 10/03/2023 - 12:00 - 13:00
MPIM Lecture Hall

Recently, a number of results have been obtained on the cohomology of Shimura varieties by studying it via a Leray spectral sequence along the Hodge-Tate period map. I will survey some of these results (some joint with Ana Caraiani, some by others) and stress in particular how they enable a study of the cohomology of the boundary. This relates to a long-standing theme of Harder's work on congruences between Eisenstein series and cusp forms, and has yielded substantial progress on the Langlands program for non-algebraic arithmetic locally symmetric spaces. If time permits, I may close with a note on another theme of this conference, motives.


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