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Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change

Part of the Progress in Mathematics Book Series (volume 298)

DOI: 10.1007/978-3-0348-0351-9

ISBN: 978-3-0348-0350-2

Publisher: Springer Basel - Springer Journals

Mar 20, 2012

1 - 10 of 11 Chapters

LitStream

Chapter 1Introduction

Getz, Jayce; Goresky, Mark

Pages: 1 –19

[In their seminal paper [Hirz] on the intersection theory of Hilbert modular surfaces, F. Hirzebruch and D. Zagier mentioned that the motivation for their work was to explain an observation of J.-P. Serre.]
LitStream

Chapter 2Review of Chains and Cochains

Getz, Jayce; Goresky, Mark

Pages: 21 –28

[Recall (e.g.,[Hud ]) that a closed convex linear cell is the convex hull of finitely many points in Euclidean space. A convex linear cell complex K is a finite collection of closed convex linear cells in some ℝN such that if 𝜎 ∈ K then every face of 𝜎 is in K, and if 𝜎, 𝜏 ∈ K then the...
LitStream

Chapter 3Review of Intersection Homology and Cohomology

Getz, Jayce; Goresky, Mark

Pages: 29 –39

[In this chapter we recall the relation between intersection homology,constructed using (p, i)-allowable chains as in [Gre4],an d intersection cohomology, constructed via sheaf theory.]
LitStream

Chapter 4Review of Arithmetic Quotients

Getz, Jayce; Goresky, Mark

Pages: 41 –55

[Possible references for the geometry described in this section include [BoS,Sa2 , Gre6,Gr e3,Gr e2].]
LitStream

Chapter 5Generalities on Hilbert Modular Forms and Varieties

Getz, Jayce; Goresky, Mark

Pages: 57 –89

[In this chapter we collect some known facts on Hilbert modular forms and varieties, mostly for the purpose of fixing our notation. These concepts will be used in Chapter 7,wh ere we will recall the description of the intersection cohomology of Hilbert modular varieties in terms of Hilbert...
LitStream

Chapter 6Automorphic Vector Bundles and Local Systems

Getz, Jayce; Goresky, Mark

Pages: 91 –110

[In this section we begin with the general theory of local systems,aut omorphic vector bundles,a nd automorphy factors. After describing the finite-dimensional representation theory of GL2 we determine the explicit equations relating modular forms and differential forms.]
LitStream

Chapter 7The Automorphic Description of Intersection Cohomology

Getz, Jayce; Goresky, Mark

Pages: 111 –134

[In this chapter we use Proposition 6.6 to construct a map \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Chapter 8Hilbert Modular Forms with Coefficients in a Hecke Module

Getz, Jayce; Goresky, Mark

Pages: 135 –150

[The goal of this chapter is to prove Theorems 8.4 and 8.5,t he full versions of Theorems 1.1 and 1.2 given in the introduction. We consider a quadratic extension of totally real number fields L/E.]
LitStream

Chapter 9Explicit Construction of Cycles

Getz, Jayce; Goresky, Mark

Pages: 151 –166

[In this chapter we consider a quadratic extension L/E of totally real fields. The inclusion E → L gives rise to Hilbert modular subvarieties,kn own as Hirzebruch- Zagier cycles, Z ⊂Y with dim(Y ) = 2 dim(Z).]
LitStream

Chapter 10The Full Version of Theorem 1.3

Getz, Jayce; Goresky, Mark

Pages: 167 –177

[We use the same setup as in the previous chapter: L/E is a quadratic extension of totally real fields \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...

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