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Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Titre(s) : Noncommutative geometry and number theory [Texte électronique] : where arithmetic meets geometry and physics / Caterina Consani, Matilde Marcolli (eds.)
Édition : 1st ed.
Publication : Wiesbaden : Vieweg, cop. 2006
Description matérielle : 1 online resource (viii, 372 pages)
Collection : Aspects of mathematics ; v. E 37
Note(s) : Includes bibliographical references
English.
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 Lfactors 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
Autre(s) auteur(s) : Consani, Caterina. Fonction indéterminée
Marcolli, Matilde. Fonction indéterminée
Max-Planck-Institut für Mathematik (Bonn). Fonction indéterminée
Sujet(s) : Géométrie différentielle non commutative
Théorie des nombres
Genre ou forme : Actes de congrès
Indice(s) Dewey : 530.156 36 (23e éd.) = Géométrie différentielle et géométrie intégrale (physique mathématique)
Identifiants, prix et caractéristiques : ISBN 9783834803528
Identifiant de la notice : ark:/12148/cb44715432c
Notice n° :
FRBNF44715432
(notice reprise d'un réservoir extérieur)
Table des matières : The Hecke algebra of a reductive p-adic group: a geometric conjecture ; Hilbert modular forms and the Ramanujan conjecture ; Farey fractions and two-dimensional tori ; Transgressions of the Godbillon-Vey Class and Rademacher functions ; Archimedean cohomology revisited ; A twisted Burnside theorem for countable groups and Reidemeister numbers ; to Hopf-Cyclic Cohomology ; The non-abelian (or non-linear) method of Chabauty ; The residues of quantum field theory ; numbers we should know ; Phase transitions with spontaneous symmetry breaking on Hecke C*-algebras from number fields ; On harmonic maps in noncommutative geometry ; Towards the fractional quantum Hall effect: a noncommutative geometry perspective ; Homological algebra for Schwartz algebras of reductive p-adic groups ; A non-commutative geometry approach to the representation theory of reductive p-adic groups: Homology of Hecke algebras, a survey and some new results ; Three examples of non-commutative boundar