Lectures on the Arithmetic Riemann-Roch Theorem
Annals of Mathematics Studies v. 127
The arithmetic Riemann-Roch theorem has been shown recently by Bismut-Gillet-Soule. 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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"This treatise provides a new approach to the arithmetic Riemann-Roch problem, and a widely algebraic-geometric method to solve it."--"Zentralblatt fur Mathematik" "