Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127

Gerd Faltings (Autor)

Buch | Softcover

118 Seiten

1992
Princeton University Press (Verlag)
978-0-691-02544-5 (ISBN)

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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.

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.

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

Erscheint lt. Verlag	10.3.1992
Reihe/Serie	Annals of Mathematics Studies
Verlagsort	New Jersey
Sprache	englisch
Maße	152 x 229 mm
Gewicht	170 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	0-691-02544-4 / 0691025444
ISBN-13	978-0-691-02544-5 / 9780691025445
Zustand	Neuware