Arakelov geometry

Author(s)

• 森脇, 淳 モリワキ, アツシ

Bibliographic Information

Arakelov geometry

Atsushi Moriwaki ; translated by Atsushi Moriwaki

（Translations of mathematical monographs, v. 244）

American Mathematical Society, 2014

Other Title

アラケロフ幾何

Arakerofu kika

Note

"First published in 2008 by Iwanami Shoten, publishers, Tokyo"--T.p. verso

Includes bibliographical references (p. 279-281) and index

Description and Table of Contents

Description

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.

Table of Contents

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

by "Nielsen BookData"

Details

• NCID: BB17212150
• ISBN:
  • 9781470410742
• LCCN: 2014021155
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: jpn
• Place of Publication: Providence, R.I.
• Pages/Volumes: ix, 285 p.
• Size: 26 cm
• Classification:
  • LCC : QA242.6
  • DC23 : 516.3/5
• Subject Headings:
  • LCSH : Arakelov theory
  • LCSH : Geometry, Algebraic
  • FREE : Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Arithmetic varieties and schemes; Arakelov theory; heights. msc
  • FREE : Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Heights. msc
  • FREE : Dynamical systems and ergodic theory -- Arithmetic and non-Archimedean dynamical systems -- Height functions; Green functions; invariant measures. msc
• Parent Bibliography ID:
  • BA00080309