Description

Book Synopsis
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. 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.

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

Arakelov Geometry

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    A Hardback by Atsushi Moriwaki

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      Publisher: MP-AMM American Mathematical
      Publication Date: Publication Date: 12/30/2014 12:00:00 AM
      ISBN13: 9781470410742, 978-1470410742
      ISBN10: 1470410745

      Description

      Book Synopsis
      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. 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.

      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

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