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

Paperback | 1992 | $60.00 | ($36.00) | £44.95 | ISBN: 9780691025445
118 pp. | 6 x 9
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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 1Classical Riemann-Roch Theorem3
Lecture 2Chern Classes of Arithmetic Vector Bundles15
Lecture 3Laplacians and Heat Kernels29
Lecture 4The Local Index Theorem for Dirac Operators44
Lecture 5Number Operators and Direct Images62
Lecture 6Arithmetic Riemann-Roch Theorem77
Lecture 7The Theorem of Bismut-Vasserot93
References99

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