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Arakelov Geometry (Translations of Mathematical Monographs)

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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.

Key Features

Arakelov Geometry (Translations of Mathematical Monographs, 244, Volume 244)

Product type: ABIS_BOOK

Brand: American Mathematical Society

Product Specifications

Colour
White
Format
hardcover
Domain
Amazon UK
Release Date
06 December 2014
Listed Since
12 September 2014

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