Adelic divisors on arithmetic varieties

著者

    • Moriwaki, Atsushi

書誌事項

Adelic divisors on arithmetic varieties

Atsushi Moriwaki

(Memoirs of the American Mathematical Society, no. 1144)

American Mathematical Society, 2016

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注記

Includes bibliographical references

"Volume 242, number 1144 (first of 4 numbers), July 2016"

内容説明・目次

内容説明

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.

目次

IntroductionPreliminariesAdelic $\mathbb{R}$-CartierDivisors over a Discrete Valuation FieldLocal and Global DensityTheoremsAdelic Arithmetic $\mathbb{R}$-CartierDivisors Continuity of the Volume Function}Zariski Decompositions of Adelic ArithmeticDivisors on Arithmetic SurfacesCharacterization of Nef Adelic Arithmetic Divisors on Arithmetic SurfacesDirichlet's unitTheorem for Adelic Arithmetic DivisorsAppendix A. Characterization of Relatively Nef Cartier DivisorsBibliographySubject IndexSymbol Index

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