1.

Record Nr.

UNINA9910154744103321

Autore

Faltings Gerd

Titolo

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

Pubbl/distr/stampa

Princeton, NJ : , : Princeton University Press, , [2016]

©1992

ISBN

1-4008-8247-8

Descrizione fisica

1 online resource (113 pages)

Collana

Annals of Mathematics Studies ; ; 309

Altri autori (Persone)

ZhangShouwu

Disciplina

516.3/5

Soggetti

Geometry, Algebraic

Riemann-Roch theorems

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

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

Sommario/riassunto

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.