Arithmetic compactifications of PEL-type Shimura varieties
By: by Kai-Wen Lan
Published: 2008
Language: eng
Number of pages: 1077
Description: In this thesis, we constructed minimal (Satake-Baily-Borel) compactifications and smooth toroidal compactifications of integral models of general PEL-type Shimura varieties (defined as in Kottwitz [79]), with descriptions of stratifications and local structures on them extending the well-known ones in the complex analytic theory. This carries out a program initiated by Chai, Faltings, and some other people more than twenty years ago. The approach we have taken is to redo the Faltings-Chai theory [37] in full generality, with as many details as possible, but without any substantial case-by-case study. The essential new ingredient in our approach is the emphasis on level structures , leading to a crucial Weil pairing calculation that enables us to avoid unwanted boundary components in naive constructions.
Notes: "May 2008."

Thesis (Ph.D., Dept. of Mathematics)--Harvard University, 2008.

Includes bibliographical references.