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Introduction

Mark Green, Phillip Griffiths, and Matt Kerr

in Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691154244
eISBN:
9781400842735
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691154244.003.0001
Subject:
Mathematics, Analysis

This book deals with Mumford-Tate groups, the fundamental symmetry groups in Hodge theory. Much, if not most, of the use of Mumford-Tate groups has been in the study of polarized Hodge structures of ... More


Hodge Representations and Hodge Domains

Mark Green, Phillip Griffiths, and Matt Kerr

in Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691154244
eISBN:
9781400842735
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691154244.003.0005
Subject:
Mathematics, Analysis

This chapter deals with Hodge representations and Hodge domains. For general polarized Hodge structures, it considers which semi-simple ℚ-algebraic groups M can be Mumford-Tate groups of polarized ... More


Period Domains and Mumford-Tate Domains

Mark Green, Phillip Griffiths, and Matt Kerr

in Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691154244
eISBN:
9781400842735
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691154244.003.0003
Subject:
Mathematics, Analysis

This chapter provides an introduction to the basic definitions of period domains and their compact duals as well as the canonical exterior differential system on them. The period domain D is ... More


Arithmetic Aspects of Mumford-Tate Domains

Mark Green, Phillip Griffiths, and Matt Kerr

in Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691154244
eISBN:
9781400842735
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691154244.003.0007
Subject:
Mathematics, Analysis

This chapter describes the arithmetic aspects of Mumford-Tate domains and Noether-Lefschetz loci. It first clarifies a few points concerning the structure and construction of Mumford-Tate domains ... More


Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

Mark Green, Phillip A. Griffiths, and Matt Kerr

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691154244
eISBN:
9781400842735
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691154244.001.0001
Subject:
Mathematics, Analysis

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 ... More


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