Faltings Lectures on the Arithmetic Riemann-Roch Theorem

1. Auflage 2016
ISBN: 978-1-4008-8247-2
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 127, 118 Seiten

Reihe: Annals of Mathematics Studies

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.

Autoren/Hrsg.

Faltings, Gerd

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

Introduction

List of Symbols

Lecture 1 Classical Riemann-Roch Theorem 3

Lecture 2 Chern Classes of Arithmetic Vector Bundles 15

Lecture 3 Laplacians and Heat Kernels 29

Lecture 4 The Local Index Theorem for Dirac Operators 44

Lecture 5 Number Operators and Direct Images 62

Lecture 6 Arithmetic Riemann-Roch Theorem 77

Lecture 7 The Theorem of Bismut-Vasserot 93

References 99