Description

Book Synopsis
The arithmetic Riemann-Roch Theorem has been shown by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. This book gives an introduction to the necessary techniques, and presents a simplified and extended version of the proof.

Trade Review
"This treatise provides a new approach to the arithmetic Riemann-Roch problem, and a widely algebraic-geometric method to solve it."--Zentralblatt fur Mathematik

Table of Contents
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

Lectures on the Arithmetic RiemannRoch Theorem

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    A Paperback / softback by Gerd Faltings

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      View other formats and editions of Lectures on the Arithmetic RiemannRoch Theorem by Gerd Faltings

      Publisher: Princeton University Press
      Publication Date: Publication Date: 10/03/1992
      ISBN13: 9780691025445, 978-0691025445
      ISBN10: 0691025444
      Also in:
      Mathematics

      Description

      Book Synopsis
      The arithmetic Riemann-Roch Theorem has been shown by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. This book gives an introduction to the necessary techniques, and presents a simplified and extended version of the proof.

      Trade Review
      "This treatise provides a new approach to the arithmetic Riemann-Roch problem, and a widely algebraic-geometric method to solve it."--Zentralblatt fur Mathematik

      Table of Contents
      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

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