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

Format:

Book

Author/Creator:

Faltings, Gerd, author.

Contributor:

Zhang, Shouwu.

Series:

Annals of mathematics studies ; no. 127.

Annals of Mathematics Studies ; 309

Language:

English

Subjects (All):

Geometry, Algebraic.

Riemann-Roch theorems.

Physical Description:

1 online resource (113 pages)

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

In English.

Summary:

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.

Contents:

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

Notes:

Includes bibliographical references.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400882472

1400882478

OCLC:

979743327