Lectures on the Arithmetic Riemann-Roch Theorem
1st Edition
Published on 20. June 2016
118 pages
978-1-4008-8247-2 (ISBN)
Description
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.
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Gerd Faltings
Lectures on the Arithmetic Riemann-Roch Theorem
Book
03/1992
Princeton University Press
€54.80
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Gerd Faltings
Lectures on the Arithmetic Riemann-Roch Theorem
Book
03/1992
Princeton University Press
€43.33
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Gerd Faltings
Content
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
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
