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.
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Höhe: 254 mm
Breite: 178 mm
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ISBN-13
978-1-4704-1926-4 (9781470419264)
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Schweitzer Klassifikation
Atsushi Moriwaki, Kyoto University, Japan.
Introduction
Preliminaries
Adelic $\mathbb{R}$-Cartier
Divisors over a Discrete Valuation Field
Local and Global Density
Theorems
Adelic Arithmetic $\mathbb{R}$-Cartier
Divisors Continuity of the Volume Function}
Zariski Decompositions of Adelic Arithmetic
Divisors on Arithmetic Surfaces
Characterization of Nef Adelic Arithmetic Divisors on Arithmetic Surfaces
Dirichlet's unit
Theorem for Adelic Arithmetic Divisors
Appendix A. Characterization of Relatively Nef Cartier Divisors
Bibliography
Subject Index
Symbol Index
