000			03524nam a22004455i 4500
001			978-3-8348-0352-8
003			DE-He213
005			20161121231036.0
007			cr nn 008mamaa
008			100301s2006 gw | s |||| 0|eng d
020			_a9783834803528 _9978-3-8348-0352-8
024	7		_a10.1007/978-3-8348-0352-8 _2doi
050		4	_aQA440-699
072		7	_aPBM _2bicssc
072		7	_aMAT012000 _2bisacsh
082	0	4	_a516 _223
245	1	0	_aNoncommutative Geometry and Number Theory _h[electronic resource] : _bWhere Arithmetic meets Geometry and Physics / _cedited by Caterina Consani, Matilde Marcolli.
264		1	_aWiesbaden : _bVieweg, _c2006.
300			_aVIII, 372 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aAspects of Mathematics, _x0179-2156
505	0		_aThe 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.
520			_aIn 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.
650		0	_aMathematics.
650		0	_aGeometry.
650	1	4	_aMathematics.
650	2	4	_aGeometry.
700	1		_aConsani, Caterina. _eeditor.
700	1		_aMarcolli, Matilde. _eeditor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783834801708
830		0	_aAspects of Mathematics, _x0179-2156
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-8348-0352-8
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c507699 _d507699