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Arithmetic compactifications of PEL-...

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Arithmetic compactifications of PEL-type Shimura varieties.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Arithmetic compactifications of PEL-type Shimura varieties./
Author:	Lan, Kai-Wen.
Description:	1077 p.
Notes:	Adviser: Richard L. Taylor.
Contained By:	Dissertation Abstracts International69-04B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3312427
ISBN:	9780549613800

Arithmetic compactifications of PEL-type Shimura varieties.
Lan, Kai-Wen.

Arithmetic compactifications of PEL-type Shimura varieties. - 1077 p.

Adviser: Richard L. Taylor.

Thesis (Ph.D.)--Harvard University, 2008.

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.

ISBN: 9780549613800Subjects--Topical Terms:

515831
Mathematics.

Arithmetic compactifications of PEL-type Shimura varieties.
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020 $a 9780549613800
035 $a (UMI)AAI3312427
035 $a AAI3312427
040 $a UMI $c UMI
100 1 $a Lan, Kai-Wen. $3 1036335
245 1 0 $a Arithmetic compactifications of PEL-type Shimura varieties.
300 $a 1077 p.
500 $a Adviser: Richard L. Taylor.
500 $a Source: Dissertation Abstracts International, Volume: 69-04, Section: B, page: 2359.
502 $a Thesis (Ph.D.)--Harvard University, 2008.
520 $a 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.
590 $a School code: 0084.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 $a Harvard University. $3 528741
773 0 $t Dissertation Abstracts International $g 69-04B.
790 $a 0084
790 1 0 $a Taylor, Richard L., $e advisor
791 $a Ph.D.
792 $a 2008
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3312427