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Adelic Divisors on Arithmetic Varieties
About this Title
Atsushi Moriwaki, Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, 606-8502, Japan
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: https://doi.org/10.1090/memo/1144
Published electronically: February 12, 2016
MSC: Primary 14G40; Secondary 11G50, 37P30
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
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.- M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0242802
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