Compactification of Siegel Moduli Schemes

doi:10.1017/CBO9780511721298

The Siegel moduli scheme classifies principally polarised abelian varieties and its compactification is an important result in arithmetic algebraic geometry. The main result of this monograph is to prove the existence of the toroidal compactification over Z (1/2). This result should have further applications and is presented here with sufficient background material to make the book suitable for seminar courses in algebraic geometry, algebraic number theory or automorphic forms.

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Compactification of Siegel Moduli Schemes

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Introduction
pp ix-xvi

Chapter I - Review of the Siegel Moduli Schemes
pp 1-63

Chapter II - Analytic Quotient Construction of Families of Degenerating Abelian Varieties
pp 64-132

Chapter III - Test Families as Coordinates at the Boundary
pp 133-158

Chapter IV - Propagation of Tai's Theorem to Positive Characteristics
pp 159-197

Chapter V - Application to Siegel Modular Forms
pp 198-211

Appendix I - Non-Symmetric Theta Constants
pp 212-236

Appendix II - Algebraic Theta Functions with Values in Complete Local Fields and Their Applications
pp 237-286

Appendix III - Stratification of Theta Closure
pp 287-314

Bibliography
pp 315-322

Index
pp 323-326

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Compactification of Siegel Moduli Schemes

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