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