Arithmetic Compactifications of PEL-type Shimura Varieties

Arithmetic Compactifications of PEL-type Shimura Varieties
Author :
Publisher : Princeton University Press
Total Pages : 587
Release :
ISBN-10 : 9780691156545
ISBN-13 : 0691156549
Rating : 4/5 (549 Downloads)

Book Synopsis Arithmetic Compactifications of PEL-type Shimura Varieties by : Kai-Wen Lan

Download or read book Arithmetic Compactifications of PEL-type Shimura Varieties written by Kai-Wen Lan and published by Princeton University Press. This book was released on 2013-03-24 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical foundation for several exciting recent developments. The book is designed to be accessible to graduate students who have an understanding of schemes and abelian varieties. PEL-type Shimura varieties, which are natural generalizations of modular curves, are useful for studying the arithmetic properties of automorphic forms and automorphic representations, and they have played important roles in the development of the Langlands program. As with modular curves, it is desirable to have integral models of compactifications of PEL-type Shimura varieties that can be described in sufficient detail near the boundary. This book explains in detail the following topics about PEL-type Shimura varieties and their compactifications: A construction of smooth integral models of PEL-type Shimura varieties by defining and representing moduli problems of abelian schemes with PEL structures An analysis of the degeneration of abelian varieties with PEL structures into semiabelian schemes, over noetherian normal complete adic base rings A construction of toroidal and minimal compactifications of smooth integral models of PEL-type Shimura varieties, with detailed descriptions of their structure near the boundary Through these topics, the book generalizes the theory of degenerations of polarized abelian varieties and the application of that theory to the construction of toroidal and minimal compactifications of Siegel moduli schemes over the integers (as developed by Mumford, Faltings, and Chai).

Arithmetic Compactifications of PEL-type Shimura Varieties Related Books

Arithmetic Compactifications of PEL-type Shimura Varieties
Language: en
Pages: 587
Authors: Kai-Wen Lan
Categories: Mathematics
Type: BOOK - Published: 2013-03-24 - Publisher: Princeton University Press

GET EBOOK

By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimur
Arithmetic Compactifications of PEL-Type Shimura Varieties
Language: en
Pages: 584
Authors: Kai-Wen Lan
Categories: Mathematics
Type: BOOK - Published: 2013-03-21 - Publisher: Princeton University Press

GET EBOOK

By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimur
Compactifications Of Pel-type Shimura Varieties And Kuga Families With Ordinary Loci
Language: en
Pages: 580
Authors: Kai-wen Lan
Categories: Mathematics
Type: BOOK - Published: 2017-07-21 - Publisher: #N/A

GET EBOOK

This book is a comprehensive treatise on the partial toroidal and minimal compactifications of the ordinary loci of PEL-type Shimura varieties and Kuga families
Compactifications of PEL-type Shimura Varieties and Kuga Families with Ordinary Loci
Language: en
Pages: 0
Authors: Kai-Wen Lan
Categories: Arithmetical algebraic geometry
Type: BOOK - Published: 2018 - Publisher: World Scientific Publishing Company

GET EBOOK

This book is a comprehensive treatise on the partial toroidal and minimal compactifications of the ordinary loci of PEL-type Shimura varieties and Kuga families
Cohomology of Arithmetic Groups
Language: en
Pages: 310
Authors: James W. Cogdell
Categories: Mathematics
Type: BOOK - Published: 2018-08-18 - Publisher: Springer

GET EBOOK

This book discusses the mathematical interests of Joachim Schwermer, who throughout his career has focused on the cohomology of arithmetic groups, automorphic f