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Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 : Annals of Mathematics Studies, 127 - Gerd Faltings

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

Annals of Mathematics Studies, 127

Paperback

Published: 10th March 1992
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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.

"This treatise provides a new approach to the arithmetic Riemann-Roch problem, and a widely algebraic-geometric method to solve it."--Zentralblatt fur Mathematik

Introductionp. vii
List of Symbolsp. ix
Classical Riemann-Roch Theoremp. 3
Chern Classes of Arithmetic Vector Bundlesp. 15
Laplacians and Heat Kernelsp. 29
The Local Index Theorem for Dirac Operatorsp. 44
Number Operators and Direct Imagesp. 62
Arithmetic Riemann-Roch Theoremp. 77
The Theorem of Bismut-Vasserotp. 93
Referencesp. 99
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780691025445
ISBN-10: 0691025444
Series: Annals of Mathematics Studies, 127
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 112
Published: 10th March 1992
Country of Publication: US
Dimensions (cm): 23.5 x 15.88  x 1.27
Weight (kg): 0.16