Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127)

Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127)

by Gerd Faltings
     
 

ISBN-10: 0691025444

ISBN-13: 9780691025445

Pub. Date: 02/19/1992

Publisher: Princeton University Press

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

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:
02/19/1992
Series:
Annals of Mathematics Studies Series, #12
Pages:
118
Product dimensions:
6.10(w) x 9.25(h) x 0.30(d)

Related Subjects

Table of Contents

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

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