Title Noncommutative geometry and number theory : where arithmetic meets geometry and physics / Caterina Consani, Matilde Marcolli (eds.)

Edition 1st ed Published Wiesbaden : Vieweg, ©2006

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Description 1 online resource (viii, 372 pages) : illustrations Series Aspects of mathematics, 0179-2156 ; v. E 37 Aspects of mathematics. E ; v. 37. 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 Summary 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 Bibliography Includes bibliographical references Notes English In Springer eBooks Subject Noncommutative differential geometry -- Congresses Number theory -- Congresses Noncommutative differential geometry. Number theory. Números , Teoría de -- Congresos Noncommutative differential geometry Number theory Genre/Form proceedings (reports) Conference papers and proceedings Conference papers and proceedings. Actes de congrès. Form Electronic book Author Consani, Caterina Marcolli, Matilde Max-Planck-Institut für Mathematik. ISBN 3834801704 9783834801708 9783834803528 3834803529

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