Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 / / Gerd Faltings.

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Faltings, Gerd,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2016]; ©1992
• Year of Publication: 2016
• Language: English
• Series: Annals of Mathematics Studies ; 127
• Physical Description: 1 online resource (118 p.)
• Other title: Frontmatter --; TABLE OF CONTENTS --; INTRODUCTION --; LIST OF SYMBOLS --; LECTURE 1. CLASSICAL RIEMANN-ROCH THEOREM --; LECTURE 2. CHERN CLASSES OF ARITHMETIC VECTOR BUNDLES --; LECTURE 3. LAPLACIANS AND HEAT KERNELS --; LECTURE 4. THE LOCAL INDEX THEOREM FOR DIRAC OPERATORS --; LECTURE 5. NUMBER OPERATORS AND DIRECT IMAGES --; LECTURE 6. ARITHMETIC RIEMANN-ROCH THEOREM --; LECTURE 7. THE THEOREM OF BISMUT-VASSEROT --; REFERENCES
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9781400882472; 9783110494914; 9783110442496
• DOI: 10.1515/9781400882472
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Gerd Faltings.

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.