Lectures on the Arithmetic Riemann-Roch Theorem

• 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

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