志甫 淳、辻 雄、斎藤 毅、
Ahmed Abbes (CNRS, IHES),
Fabrice Orgogozo (CNRS, Ecole Polytechnique),
田 野 (Tian Ye),
田 一超(Tian Yichao, Morningside center, HIM Bonn)、
鄭 維哲(Zheng Weizhe, Morningside center)
W. Niziol (CNRS & ENS de Lyon)
I will present a proof of a comparison isomorphism, up to some universal constants, between truncated sheaves of p-adic nearby cycles and syntomic cohomology sheaves on semistable schemes over a mixed characteristic local rings. This generalizes the comparison results of Kato, Kurihara, and Tsuji for small Tate twists (where no constants are necessary) as well as the comparison result of Tsuji that holds over the algebraic closure of the field. This is a joint work with Pierre Colmez.
Syntomic complexes and p-adic nearby cycles
Xu Shen(申旭) (Morningside Center of Mathematics)
Local and global geometric structures of perfectoid Shimura varieties
In this talk, we will investigate some geometric structural properties of perfectoid Shimura varieties of abelian type. In the global part, we will construct some minimal and toroidal type compactifications for these spaces, and we will describe explicitly the degeneration of Hodge-Tate period map at the boundaries. In the local part, we will show that each Newton stratum of these perfectoid Shimura varieties can be described by the related (generalized) Rapoport-Zink space and Igusa variety. As a consequence of our local and global constructions, we can compute the stalks of the relative cohomology under the Hodge-Tate period map of the intersection complex (on the minimal compactification), in terms of cohomology of Igusa varieties at the boundary with truncated coefficients.