**Memoirs of the American Mathematical Society**

2016;
122 pp;
Softcover

MSC: Primary 14;
Secondary 11; 37

**Print ISBN: 978-1-4704-1926-4
Product Code: MEMO/242/1144**

List Price: $84.00

AMS Member Price: $50.40

MAA Member Price: $75.60

**Electronic ISBN: 978-1-4704-2942-3
Product Code: MEMO/242/1144.E**

List Price: $84.00

AMS Member Price: $50.40

MAA Member Price: $75.60

# Adelic Divisors on Arithmetic Varieties

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*Atsushi Moriwaki*

In this article, the author generalizes several fundamental results for arithmetic divisors, such as the continuity of the volume function, the generalized Hodge index theorem, Fujita's approximation theorem for arithmetic divisors, Zariski decompositions for arithmetic divisors on arithmetic surfaces and a special case of Dirichlet's unit theorem on arithmetic varieties, to the case of the adelic arithmetic divisors.

#### Table of Contents

# Table of Contents

## Adelic Divisors on Arithmetic Varieties

- Cover Cover11
- Title page i2
- Introduction 18
- Chapter 1. Preliminaries 916
- Chapter 2. Adelic ℝ-Cartier Divisors over a Discrete Valuation Field 2330
- Chapter 3. Local and Global Density Theorems 3744
- Chapter 4. Adelic Arithmetic ℝ-Cartier Divisors 4552
- Chapter 5. Continuity of the Volume Function 6168
- Chapter 6. Zariski Decompositions of Adelic Arithmetic Divisors on Arithmetic Surfaces 7582
- Chapter 7. Characterization of Nef Adelic Arithmetic Divisors on Arithmetic Surfaces 8794
- Chapter 8. Dirichlet’s unit Theorem for Adelic Arithmetic Divisors 99106
- Appendix A. Characterization of Relatively Nef Cartier Divisors 107114
- Bibliography 117124
- Subject Index 119126
- Symbol Index 121128
- Back Cover Back Cover1134