Lectures on the arithmetic Riemann-Roch theorem

✍ Scribed by Gerd Faltings

• Publisher: Princeton University Press
• Year: 1992
• Tongue: English
• Leaves: 107
• Series: AM-127
• Edition: Limited Ed
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Table of Contents......Page 2
INTRODUCTION......Page 4
LIST OF SYMBOLS......Page 6
LECTURE 1. CLASSICAL RIEMANN-ROCH THEOREM ......Page 10
LECTURE 2. CHERN CLASSES OF ARITHMETIC VECTOR BUNDLES ......Page 22
LECTURE 3. LAPLACIANS AND HEAT KERNELS ......Page 36
LECTURE 4. THE LOCAL INDEX THEOREM FOR DIRAC OPERATORS ......Page 51
LECTURE 5. NUMBER OPERATORS AND DIRECT IMAGES ......Page 69
LECTURE 6. ARITHMETIC RIEMANN-ROCH THEOREM ......Page 84
LECTURE 7. THE THEOREM OF BISMUT-VASSEROT ......Page 100
REFERENCES ......Page 106