Lectures on the Arithmetic Riemann-Roch Theorem

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ISBN: 9780691025445 | 0691025444
Cover: Paperback
Copyright: 2/19/1992

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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.

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Introduction	p. vii
List of Symbols	p. ix
Classical Riemann-Roch Theorem	p. 3
Chern Classes of Arithmetic Vector Bundles	p. 15
Laplacians and Heat Kernels	p. 29
The Local Index Theorem for Dirac Operators	p. 44
Number Operators and Direct Images	p. 62
Arithmetic Riemann-Roch Theorem	p. 77
The Theorem of Bismut-Vasserot	p. 93
References	p. 99
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Lectures on the Arithmetic Riemann-Roch Theorem

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