Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127

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.