In this paper, we study the basic locus in the fiber at $p$ of a certain unitary Shimura variety with a certain parahoric level structure. The basic locus $\widehat{\CM^{ss}}$ is uniformized by a formal scheme $\CN$ which is called Rapoport-Zink space. We show that the irreducible components of the induced reduced subscheme $\CN_{red}$ of $\CN$ are Deligne-Lusztig varieties and their intersection behavior is controlled by a certain Bruhat-Tits building. Also, we define special cycles in $\CN$ and study their intersection multiplicities.

Creator

• Cho, Sungyoon

DOI

• https://doi.org/10.21985/n2-9fh9-v436

Subject

• Mathematics

Language

• en

Alternate Identifier

• http://dissertations.umi.com/northwestern:14572
• etdadmin_upload_657697

Date created

• 2019-01-01

Resource type

• Dissertation

Rights statement

• In Copyright