Amazon cover image
Image from Amazon.com

Noncommutative Geometry and Number Theory [electronic resource] : Where Arithmetic meets Geometry and Physics / edited by Caterina Consani, Matilde Marcolli.

Contributor(s): Consani, Caterina [editor.] | Marcolli, Matilde [editor.] | SpringerLink (Online service)Material type: TextTextSeries: Aspects of MathematicsPublisher: Wiesbaden : Vieweg, 2006Description: VIII, 372 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783834803528Subject(s): Mathematics | Geometry | Mathematics | GeometryAdditional physical formats: Printed edition:: No titleDDC classification: 516 LOC classification: QA440-699Online resources: Click here to access online
Contents:
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 boundaries of Shimura varieties -- Holomorphic bundles on 2-dimensional noncommutative toric orbifolds -- A New short proof of the local index formula of Atiyah-Singer.
In: Springer eBooksSummary: 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.
Tags from this library: No tags from this library for this title. Log in to add tags.
Star ratings
    Average rating: 0.0 (0 votes)
Holdings
Item type Current library Collection Call number Status Date due Barcode Item holds
eBook eBook e-Library

Electronic Book@IST

EBook Available
Total holds: 0

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 boundaries of Shimura varieties -- Holomorphic bundles on 2-dimensional noncommutative toric orbifolds -- A New short proof of the local index formula of Atiyah-Singer.

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.

Powered by Koha