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

Paper | 1992 | $37.00 / £25.95
118 pp.

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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.

Review:

"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

Series:

• Annals of Mathematics Studies
  Phillip A. Griffiths, John N. Mather, and Elias M. Stein, Editors

Subject Area:

• Mathematics

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For customers in the U.S., Canada, Latin America, Asia, and Australia
Paper: $37.00 ISBN13: 978-0-691-02544-5

For customers in Europe, Africa, the Middle East, and India
Paper: £25.95 ISBN13: 978-0-691-02544-5

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