Lectures on the Arithmetic Riemann-Roch Theorem
Lectures on the Arithmetic Riemann-Roch Theorem by Gerd Faltings, published by Princeton University Press on March 10, 1992, is a limited edition work comprising 100 pages in English. This book provides a concise introduction to the arithmetic Riemann-Roch Theorem, which has been recently proven by Bismut-Gillet-Soul. It aims to present a simplified and extended version of the proof, integrating concepts from algebra, arithmetic, and analysis.
Readers will find that this book equips mathematicians with a background in arithmetic algebraic geometry with essential techniques relevant to the evolving field of Arakelov-theory. The text focuses on the necessary methodologies to grasp the theorem’s implications and applications within mathematical analysis and geometry. This edition serves as a valuable resource for those looking to deepen their understanding of these advanced mathematical concepts.
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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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