# Special Values of Automorphic Cohomology Classes

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*Mark Green; Phillip Griffiths; Matt Kerr*

#### Table of Contents

# Table of Contents

## Special Values of Automorphic Cohomology Classes

- Cover Cover11 free
- Title page i2 free
- Introduction 18 free
- Chapter I. Geometry of the Mumford-Tate domains 1724
- Chapter II. Homogeneous line bundles over the Mumford-Tate domains 3744
- Chapter III. Correspondence and cycle spaces; Penrose transforms 4956
- III.A. Introduction 4956
- III.B. Basic definitions and examples 4956
- III.C. The basic example 5966
- III.D. The Penrose transform in the compact case 6875
- Appendix to section III.D: Arithmetic aspects of the Penrose transform in the compact case 7380
- III.E. The Penrose transform in the first example 7784
- III.F. The Penrose transform in the second example 8693

- Chapter IV. The Penrose transform in the automorphic case and the main result 93100
- IV.A. Cuspidal automorphic cohomology 93100
- IV.B. Picard and Siegel cuspidal automorphic forms 98105
- IV.C. Arithmetic structures on vector spaces 102109
- Appendix to section IV.C: Explicit canonical models for the two examples 108115
- IV.D. Special values of cuspidal automorphic cohomology classes 110117
- Appendix to section IV.D: An alternate method for evaluating cohomology classes and a question 113120
- IV.E. CM points on correspondence spaces 117124
- IV.F. On a result of Carayol 123130
- Appendix to section IV.F: Geometric construction of 𝐾-types and discussion of totally degenerate limits of discrete series 130137

- Bibliography 143150
- Back Cover Back Cover1158