Lectures on the Arithmetic Riemann-Roch Theorem - Brossura

Faltings, Gerd

Brossura

ISBN 10: 0691025444 ISBN 13: 9780691025445

Casa editrice: Princeton Univ Pr, 1992

Riassunto

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.

Su questo libro

Recensione:

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

Contenuti:

	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

Su questa edizione

• Editore: Princeton Univ Pr
• Data di pubblicazione: 1992
• ISBN 10: 0691025444
• ISBN 13: 9780691025445
• Rilegatura: Copertina flessibile
• Numero di pagine: 112