Electronic ISBN:  9781470429423 
Product Code:  MEMO/242/1144.E 
List Price:  $84.00 
MAA Member Price:  $75.60 
AMS Member Price:  $50.40 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 242; 2016; 122 ppMSC: Primary 14; Secondary 11; 37;
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

Chapters

Introduction

1. Preliminaries

2. Adelic $\mathbb {R}$Cartier Divisors over a Discrete Valuation Field

3. Local and Global Density Theorems

4. Adelic Arithmetic $\mathbb {R}$Cartier Divisors

5. Continuity of the Volume Function

6. Zariski Decompositions of Adelic Arithmetic Divisors on Arithmetic Surfaces

7. Characterization of Nef Adelic Arithmetic Divisors on Arithmetic Surfaces

8. Dirichlet’s unit Theorem for Adelic Arithmetic Divisors

A. Characterization of Relatively Nef Cartier Divisors


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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.

Chapters

Introduction

1. Preliminaries

2. Adelic $\mathbb {R}$Cartier Divisors over a Discrete Valuation Field

3. Local and Global Density Theorems

4. Adelic Arithmetic $\mathbb {R}$Cartier Divisors

5. Continuity of the Volume Function

6. Zariski Decompositions of Adelic Arithmetic Divisors on Arithmetic Surfaces

7. Characterization of Nef Adelic Arithmetic Divisors on Arithmetic Surfaces

8. Dirichlet’s unit Theorem for Adelic Arithmetic Divisors

A. Characterization of Relatively Nef Cartier Divisors