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

Paperback | 1992 | $60.00 | £49.95 | ISBN: 9780691025445
118 pp. | 6 x 9
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eBook | ISBN: 9781400882472 |
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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.

Reviews:

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

Table of Contents:

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

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