Lectures on the Arithmetic Riemann-Roch Theorem

By Walter H. Beale

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.

• Format: Paperback
• Language: English
• ISBN: 0691025444
• ISBN13: 9780691025445
• Release Date: February 1992
• Publisher: Princeton University Press
• Length: 118 Pages
• Weight: 0.35 lbs.
• Dimensions: 0.3" x 6.1" x 9.3"

Customer Reviews

Deep but important

The Riemann-Roch theorem has come a long way since its origins in the work of Bernhard Riemann 154 years ago. Riemann was attempting to establish the existence of complex functions on multiply-connected surfaces with no boundary. A surface that is (2p + 1)-connected for a positive integer p can be represented as a 4p-sided polygon after making 2p cuts. Riemann showed using the Dirichlet principle that there are p linearly-independent...