Mumford-Tate groups and domains : their geometry and arithmetic / Mark Green, Phillip Griffiths, Matt Kerr.

Format:

Book

Author/Creator:

Green, M. (Mark)

Contributor:

Griffiths, Phillip, 1938-

Kerr, Matthew D., 1975-

Series:

Annals of mathematics studies ; no. 183.

Annals of mathematics studies ; no. 183

Language:

English

Subjects (All):

Mumford-Tate groups.

Geometry, Algebraic.

Physical Description:

1 online resource (298 p.)

Edition:

Course Book

Place of Publication:

Princeton : Princeton University Press, 2012.

Language Note:

English

Summary:

Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the nonclassical case. The general theory turns out to be very rich, such as in the unexpected connections of finite dimensional and infinite dimensional representation theory of real, semisimple Lie groups. The authors give the complete classification of Hodge representations, a topic that should become a standard in the finite-dimensional representation theory of noncompact, real, semisimple Lie groups. They also indicate that in the future, a connection seems ready to be made between Lie groups that admit discrete series representations and the study of automorphic cohomology on "ients of Mumford-Tate domains by arithmetic groups. Bringing together complex geometry, representation theory, and arithmetic, this book opens up a fresh perspective on an important subject.

Contents:

Frontmatter

Contents

Introduction

Chapter I. Mumford-Tate Groups

Chapter II. Period Domains and Mumford-Tate Domains

Chapter III. The Mumford-Tate Group of a Variation of Hodge Structure

Chapter IV. Hodge Representations and Hodge Domains

Chapter V. Hodge Structures With Complex Multiplication

Chapter VI. Arithmetic Aspects of Mumford-Tate Domains

Chapter VII. Classification of Mumford-Tate Subdomains

Chapter VIII. Arithmetic of Period Maps of Geometric Origin

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786613589880

9781280494659

1280494654

9781400842735

1400842735

OCLC:

854968413