Thursday 13 Nov 2014: Rapoport-Zink spaces of Hodge type and application to Shimura varieties
Wansu Kim - University of Cambridge
Rapoport-Zink spaces of (P)EL type are local analogues of Shimura varieties of PEL type. Examples include Lubin-Tate spaces and Drinfeld upper half spaces. Rapoport-Zink spaces play an important role the local Langlands and Jacquet-Langlands correspondences, and the study of mod p geometry of PEL Shimura varieties.
In this talk, we construct the "Hodge-type generalisation" of Rapoport-Zink spaces under the unramifiedness hypothesis, and apply it to the integral models of Hodge-type Shimura varieties. The new examples are Spin and orthogonal Rapoport-Zink spaces (of arbitrary rank) -- local analogues of Spin and orthogonal Shimura varieties.
We will start with the description of geometric points of "Hodge-type Rapoport-Zink spaces" and the completed local rings thereof.