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Atsushi Moriwaki Kyoto University, Kyoto, Japan
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Electronic ISBN: 978-1-4704-2942-3
Product Code: MEMO/242/1144.E
List Price: $84.00 MAA Member Price:$75.60
AMS Member Price: $50.40 Click above image for expanded view Adelic Divisors on Arithmetic Varieties Atsushi Moriwaki Kyoto University, Kyoto, Japan Available Formats:  Electronic ISBN: 978-1-4704-2942-3 Product Code: MEMO/242/1144.E  List Price:$84.00 MAA Member Price: $75.60 AMS Member Price:$50.40
• Book Details

Memoirs of the American Mathematical Society
Volume: 2422016; 122 pp
MSC: 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.

• 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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Review Copy – for reviewers who would like to review an AMS book
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Volume: 2422016; 122 pp
MSC: 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.

• 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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