Arakelov geometry
著者
書誌事項
Arakelov geometry
（Translations of mathematical monographs, v. 244）
American Mathematical Society, 2014
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アラケロフ幾何
Arakerofu kika
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注記
"First published in 2008 by Iwanami Shoten, publishers, Tokyo"--T.p. verso
Includes bibliographical references (p. 279-281) and index
内容説明・目次
内容説明
The main goal of this book is to present the so-called birational Arakelov geometry, which can be viewed as an arithmetic analog of the classical birational geometry, i.e., the study of big linear series on algebraic varieties. After explaining classical results about the geometry of numbers, the author starts with Arakelov geometry for arithmetic curves, and continues with Arakelov geometry of arithmetic surfaces and higher-dimensional varieties. The book includes such fundamental results as arithmetic Hilbert-Samuel formula, arithmetic Nakai-Moishezon criterion, arithmetic Bogomolov inequality, the existence of small sections, the continuity of arithmetic volume function, the Lang-Bogomolov conjecture and so on. In addition, the author presents, with full details, the proof of Faltings' Riemann-Roch theorem.
Prerequisites for reading this book are the basic results of algebraic geometry and the language of schemes.
目次
Preliminaries
Geometry of numbers
Arakelov geometry on arithmetic curves
Arakelov geometry on arithmetic surfaces
Arakelov geometry on general arithmetic varieties
Arithmetic volume function and its continuity
Nakai-Moishezon criterion on an arithmetic variety
Arithmetic Bogomolov inequality
Lang-Bogomolov conjecture
Bibliography
Index
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