Irreducible components of affine Deligne-Lusztig varieties

Abstract: Affine Deligne-Lusztig varieties naturally arise from the study of Shimura varieties. We prove a formula for the number of their irreducible components, which was a conjecture of Miaofen Chen and Xinwen Zhu. Our method is to count the number of F_q points, and to relate it to certain twisted orbital integrals. We then study the growth rate of these integrals using the Base Change Fundamental Lemma of Clozel and Labesse. In an ongoing work we also give the number of irreducible components in the basic Newton stratum of a Shimura variety. This is joint work with Rong Zhou and Xuhua He.

number theory

Audience: researchers in the topic

University of Arizona Algebra and Number Theory Seminar