Twisted orbital integrals and irreducible components of affine Deligne-Lusztig varieties

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• Rong Zhou (Imperial College London)
• Tuesday 04 February 2020, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Jessica Fintzen.

Affine Deligne-Lusztig varieties (ADLV) naturally arise in the study of Shimura varieties and Rapoport-Zink spaces; their irreducible components give rise to an interesting class of cycles on the special fiber of Shimura varieties. In a joint work with Y. Zhu, we give a description of the top-dimensional irreducible components of ADLV ’s modulo the action of a natural symmetry group, verifying a conjecture of M. Chen and X. Zhu. In a work in progress with X. He and Y. Zhu, we use the previous result to obtain a description of the irreducible components of the basic locus of certain Shimura varieties in terms of a class set for an inner form of the structure group, generalizing classical results of Deuring and Serre. A key input for our approach is an analysis of certain twisted orbital integrals using techniques from local harmonic analysis.

This talk is part of the Number Theory Seminar series.

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