Arithmetic Compactifications Of Pel Type Shimura Varieties
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Author | : Kai-Wen Lan |
Publisher | : Princeton University Press |
Total Pages | : 587 |
Release | : 2013-03-24 |
Genre | : Mathematics |
ISBN | : 0691156549 |
Download Arithmetic Compactifications of PEL-type Shimura Varieties Book in PDF, Epub and Kindle
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).
Author | : Kai-wen Lan |
Publisher | : #N/A |
Total Pages | : 580 |
Release | : 2017-07-21 |
Genre | : Mathematics |
ISBN | : 9813207345 |
Download Compactifications Of Pel-type Shimura Varieties And Kuga Families With Ordinary Loci Book in PDF, Epub and Kindle
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, and on the canonical and subcanonical extensions of automorphic bundles. The results in this book serve as the logical foundation of several recent developments in the theory of p-adic automorphic forms; and of the author's work with Harris, Taylor, and Thorne on the construction of Galois representations without any polarizability conditions, which is a major breakthrough in the Langlands program.This book is important for active researchers and graduate students who need to understand the above-mentioned recent works, and is written with such users of the theory in mind, providing plenty of explanations and background materials, which should be helpful for people working in similar areas. It also contains precise internal and external references, and an index of notation and terminologies. These are useful for readers to quickly locate materials they need.
Author | : Kai-Wen Lan |
Publisher | : Princeton University Press |
Total Pages | : 584 |
Release | : 2013-03-21 |
Genre | : Mathematics |
ISBN | : 1400846013 |
Download Arithmetic Compactifications of PEL-Type Shimura Varieties Book in PDF, Epub and Kindle
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).
Author | : Thomas Haines |
Publisher | : Cambridge University Press |
Total Pages | : 341 |
Release | : 2020-02-20 |
Genre | : Mathematics |
ISBN | : 1108704867 |
Download Shimura Varieties Book in PDF, Epub and Kindle
This volume forms the sequel to "On the stabilization of the trace formula", published by International Press of Boston, Inc., 2011
Author | : Fritz Hörmann |
Publisher | : |
Total Pages | : 152 |
Release | : 2014 |
Genre | : Arithmetical algebraic geometry |
ISBN | : 9781470419585 |
Download The Geometric and Arithmetic Volume of Shimura Varieties of Orthogonal Type Book in PDF, Epub and Kindle
Cover -- Title page -- Contents -- Overview -- Integral models of toroidal compactifications of mixed Shimura varieties -- Volumes of orthogonal Shimura varieties -- Appendix A -- Appendix B -- Bibliography -- Index -- Table of notation -- Back Cover
Author | : Fritz Hörmann |
Publisher | : |
Total Pages | : 273 |
Release | : 2010 |
Genre | : |
ISBN | : |
Download The Arithmetic Volume of Shimura Varieties of Orthogonal Type Book in PDF, Epub and Kindle
Author | : Richard Pink |
Publisher | : |
Total Pages | : 0 |
Release | : 1990 |
Genre | : Abelian varieties |
ISBN | : |
Download Arithmetical compactification of mixed Shimura varieties Book in PDF, Epub and Kindle
Author | : Mafalda Milheiro Marques da Silva Santos |
Publisher | : |
Total Pages | : 0 |
Release | : 2023 |
Genre | : |
ISBN | : |
Download On the Generic Part of the Cohomology of Non-compact PEL-type A Shimura Varieties Book in PDF, Epub and Kindle
Author | : James W. Cogdell |
Publisher | : Springer |
Total Pages | : 304 |
Release | : 2018-08-18 |
Genre | : Mathematics |
ISBN | : 3319955497 |
Download Cohomology of Arithmetic Groups Book in PDF, Epub and Kindle
This book discusses the mathematical interests of Joachim Schwermer, who throughout his career has focused on the cohomology of arithmetic groups, automorphic forms and the geometry of arithmetic manifolds. To mark his 66th birthday, the editors brought together mathematical experts to offer an overview of the current state of research in these and related areas. The result is this book, with contributions ranging from topology to arithmetic. It probes the relation between cohomology of arithmetic groups and automorphic forms and their L-functions, and spans the range from classical Bianchi groups to the theory of Shimura varieties. It is a valuable reference for both experts in the fields and for graduate students and postdocs wanting to discover where the current frontiers lie.
Author | : Richard Shadrach |
Publisher | : |
Total Pages | : 174 |
Release | : 2014 |
Genre | : Electronic dissertations |
ISBN | : 9781303938948 |
Download Integral Models of Certain PEL Shimura Varieties with Gamma 1(p)-type Level Structure Book in PDF, Epub and Kindle