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Hodge Structures with Complex Multiplication

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/9780691154244.003.0006
Subject:
Mathematics, Analysis

This chapter describes Hodge structures with a high degree of symmetry, and specifically complex multiplication Hodge structures or CM Hodge structures. It broadens the notion of CM type by defining ... More


Classification of Mumford-Tate Subdomains

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/9780691154244.003.0008
Subject:
Mathematics, Analysis

This chapter develops an algorithm for determining all Mumford-Tate subdomains of a given period domain. The result is applied to the classification of all complex multiplication Hodge structures (CM ... More


Arithmetic of Period Maps of Geometric Origin

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/9780691154244.003.0009
Subject:
Mathematics, Analysis

This chapter considers some arithmetic aspects of period maps with a geometric origin. It focuses on the situation Φ‎ : S(ℂ) → Γ‎\D, where S parametrizes a family X → S of smooth, projective ... More


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