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# memo_has_moved_text();Adelic Divisors on Arithmetic Varieties

Atsushi Moriwaki

Publication: Memoirs of the American Mathematical Society
Publication Year: 2016; Volume 242, Number 1144
ISBNs: 978-1-4704-1926-4 (print); 978-1-4704-2942-3 (online)
DOI: http://dx.doi.org/10.1090/memo/1144
Published electronically: February 12, 2016

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Chapters

• Introduction
• Chapter 1. Preliminaries
• Chapter 2. Adelic $\mathbb R$-Cartier Divisors over a Discrete Valuation Field
• Chapter 3. Local and Global Density Theorems
• Chapter 4. Adelic Arithmetic $\mathbb R$-Cartier Divisors
• Chapter 5. Continuity of the Volume Function
• Chapter 6. Zariski Decompositions of Adelic Arithmetic Divisors on Arithmetic Surfaces
• Chapter 7. Characterization of Nef Adelic Arithmetic Divisors on Arithmetic Surfaces
• Chapter 8. Dirichlet’s unit Theorem for Adelic Arithmetic Divisors
• Appendix A. Characterization of Relatively Nef Cartier Divisors

### Abstract

In this article, we generalize 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.