Lectures on the Arithmetic Riemann-Roch Theorem

Erscheinungsjahr 1992
ISBN: 978-0-691-02544-5
Verlag: Princeton University Press

Buch, Englisch, Band (AM-127), 118 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 175 g

Reihe: Annals of Mathematics Studies

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.

Autoren/Hrsg.

Faltings, Gerd

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

IntroductionList of SymbolsLecture 1Classical Riemann-Roch Theorem3Lecture 2Chern Classes of Arithmetic Vector Bundles15Lecture 3Laplacians and Heat Kernels29Lecture 4The Local Index Theorem for Dirac Operators44Lecture 5Number Operators and Direct Images62Lecture 6Arithmetic Riemann-Roch Theorem77Lecture 7The Theorem of Bismut-Vasserot93References99