000			03649nam a22005055i 4500
001			978-1-4471-4393-2
003			DE-He213
005			20140220083237.0
007			cr nn 008mamaa
008			120905s2012 xxk| s |||| 0|eng d
020			_a9781447143932 _9978-1-4471-4393-2
024	7		_a10.1007/978-1-4471-4393-2 _2doi
050		4	_aQA612.33
072		7	_aPBPD _2bicssc
072		7	_aMAT002010 _2bisacsh
082	0	4	_a512.66 _223
100	1		_aDundas, Bjørn Ian. _eauthor.
245	1	4	_aThe Local Structure of Algebraic K-Theory _h[electronic resource] / _cby Bjørn Ian Dundas, Thomas G. Goodwillie, Randy McCarthy.
264		1	_aLondon : _bSpringer London : _bImprint: Springer, _c2012.
300			_aXV, 435 p. 5 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aAlgebra and Applications, _x1572-5553 ; _v18
505	0		_aAlgebraic K-theory -- Gamma-spaces and S-algebras -- Reductions -- Topological Hochschild Homology -- The Trace K → THH -- Topological Cyclic Homology -- The Comparison of K-theory and TC.
520			_aAlgebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.
650		0	_aMathematics.
650		0	_aAlgebra.
650		0	_aK-theory.
650		0	_aAlgebraic topology.
650	1	4	_aMathematics.
650	2	4	_aK-Theory.
650	2	4	_aAlgebraic Topology.
650	2	4	_aCategory Theory, Homological Algebra.
700	1		_aGoodwillie, Thomas G. _eauthor.
700	1		_aMcCarthy, Randy. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781447143925
830		0	_aAlgebra and Applications, _x1572-5553 ; _v18
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4471-4393-2
912			_aZDB-2-SMA
999			_c100785 _d100785