Lectures on the Arithmetic Riemann-Roch Theorem
The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in arithmetic algebraic geometry to understand some basic techniques in the rapidly evolving field of Arakelov-theory.

1119055870
Lectures on the Arithmetic Riemann-Roch Theorem
The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in arithmetic algebraic geometry to understand some basic techniques in the rapidly evolving field of Arakelov-theory.

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Lectures on the Arithmetic Riemann-Roch Theorem

Lectures on the Arithmetic Riemann-Roch Theorem

by Gerd Faltings
Lectures on the Arithmetic Riemann-Roch Theorem

Lectures on the Arithmetic Riemann-Roch Theorem

by Gerd Faltings

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Overview

The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in arithmetic algebraic geometry to understand some basic techniques in the rapidly evolving field of Arakelov-theory.


Product Details

ISBN-13: 9780691025445
Publisher: Princeton University Press
Publication date: 03/10/1992
Series: Annals of Mathematics Studies , #127
Pages: 118
Product dimensions: 6.00(w) x 9.00(h) x (d)

Table of Contents

Introductionvii
List of Symbolsix
Lecture 1.Classical Riemann-Roch Theorem3
Lecture 2.Chern Classes of Arithmetic Vector Bundles15
Lecture 3.Laplacians and Heat Kernels29
Lecture 4.The Local Index Theorem for Dirac Operators44
Lecture 5.Number Operators and Direct Images62
Lecture 6.Arithmetic Riemann-Roch Theorem77
Lecture 7.The Theorem of Bismut-Vasserot93
References99
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