Consani / Marcolli Noncommutative Geometry and Number Theory

Where Arithmetic meets Geometry and Physics
2006
ISBN: 978-3-8348-0352-8
Verlag: Vieweg & Teubner
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 372 Seiten, eBook

Reihe: Aspects of Mathematics

In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Consani, Caterina

Marcolli, Matilde

Weitere Mitwirkende

Diederich, Klas

Inhaltsverzeichnis

The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.

Über Autor(innen)

Prof. Dr. Caterina Consani, Department of Mathematics, The Johns Hopkins University, Baltimore, USA
Prof. Dr. Matilde Marcolli, Max-Planck Institute for Mathematics, Bonn, Germany