Lectures on the Arithmetic Riemann-Roch Theorem

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Princeton University Press, Mar 10, 1992 - Mathematics - 100 pages

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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Contents

CLASSICAL RIEMANNROCH THEOREM
3
CHERN CLASSES OF ARITHMETIC VECTOR BUNDLES
15
LAPLACIANS AND HEAT KERNELS
29
THE LOCAL INDEX THEOREM FOR DIRAC OPERATORS
44
NUMBER OPERATORS AND DIRECT IMAGES
62
ARITHMETIC RIEMANNROCH THEOREM
77
THE THEOREM OF BISMUTVASSEROT
93
REFERENCES
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