Noncommutative Geometry and Number Theory

Caterina Consani

ISBN 10: 3834826731 / ISBN 13: 9783834826732

Published by Vieweg & Teubner Verlag Dez 2014, 2014

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 380 pp. Englisch.

Seller Inventory # 9783834826732

Bibliographic Details

• Title: Noncommutative Geometry and Number Theory
• Publisher: Vieweg & Teubner Verlag Dez 2014
• Publication Date: 2014
• Language: English
• ISBN 10: 3834826731
• ISBN 13: 9783834826732
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 240W x 168H x 21D millimeters 240 millimeters width by 168 millimeters height by 21 millimeters depth
• Weight: 636 grams

About this title

Synopsis

In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. Research across these ?elds has now reached an imp- tant turning point, as shows the increasing interest with which the mathematical community approaches these topics. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new c- nections between the ?elds of number theory, algebraic geometry and noncom- tative geometry. Thecontributionstothisvolumepartlyre?ectthetwoworkshops“Noncom- tative Geometry and Number Theory” that took place at the Max–Planck–Institut f¨ ur Mathematik in Bonn, in August 2003 and June 2004. The two workshops were the ?rst activity entirely dedicated to the interplay between these two ?elds of mathematics. An important part of the activities, which is also re?ected in this volume, came from the hindsight of physics which often provides new perspectives onnumber theoretic problems that make it possible to employ the tools of nonc- mutative geometry, well designed to describe the quantum world.

About the Author

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