Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)
Mark Green, Phillip A. Griffiths, and Matt Kerr
Abstract
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 is 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. ... More
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 is 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 book gives 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. It also indicates 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 quotients 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.
Keywords:
algebraic geometry,
Mumford-Tate group,
Hodge theory,
semisimple Lie group,
Lie group,
automorphic cohomology,
Mumford-Tate domain,
Hodge representation,
arithmetic group
Bibliographic Information
| Print publication date: 2012 |
Print ISBN-13: 9780691154244 |
| Published to Princeton Scholarship Online: October 2017 |
DOI:10.23943/princeton/9780691154244.001.0001 |
Authors
Affiliations are at time of print publication.
Mark Green, author
University of California, Los Angeles
Phillip A. Griffiths, author
Institute for Advanced Study
Matt Kerr, author
Washinton University
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