


Lectures on the Arithmetic RiemannRoch Theorem. (AM127) 
The arithmetic RiemannRoch Theorem has been shown recently by BismutGilletSoul. 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 Arakelovtheory. "This treatise provides a new approach to the arithmetic RiemannRoch problem, and a widely algebraicgeometric method to solve it."Zentralblatt für Mathematik
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