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Arithmetic compactifications of PEL-type Shimura varieties (2010)
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@MISC{Lan10arithmeticcompactifications,
author = {Kai-wen Lan},
title = {Arithmetic compactifications of PEL-type Shimura varieties },
year = {2010}
}
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Abstract
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 [72]), 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 [39] 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.
Keyphrases
pel-type shimura variety arithmetic compactifications naive construction crucial weil level structure many detail well-known one smooth toroidal compactifications integral model essential new ingredient full generality substantial case-by-case study local structure general pel-type shimura variety unwanted boundary component faltings-chai theory complex analytic theory
