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Mass formulas and the basic locus of unitary Shimura varieties


余家富 研究员(中研院数学所)



腾讯会议 会议号:547 578 754


The supersingular locus of modular varieties has been playing an important role in geometry, arithmetic and the theory of automorphic forms. The geometry and arithmetic has been studied by Deuring, Ibukiyama, Katsura, Li and Oort. In this talk we shall discuss the geometry and arithmetic of the basic locus (that is, the unique smallest Newton stratum) of the Shimura variety attached to GU(r,s). These have been investigated by Vollaard, Wedhorn and very recently by X. He, Z. Rong, Y. Zhou, X. Zhu, and the geometry of its p-adic variant (basic affine Deligne-Lusztig varieties) by He, Gortz, M. Chen, Hamacher, Viehman and Nie. We shall report explicit formulas for the number of irreducible components, the size of the zero-dimensional EO stratum, and the number of irreducible components of each basic EO stratum for (r,s)=(1,n-1). This is based on the joint work with Yasuhiro Terakado.