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001 978-3-642-29514-0
003 DE-He213
005 20140220083316.0
007 cr nn 008mamaa
008 120712s2012 gw | s |||| 0|eng d
020 _a9783642295140
_9978-3-642-29514-0
024 7 _a10.1007/978-3-642-29514-0
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
082 0 4 _a516.35
_223
100 1 _aMorel, Fabien.
_eauthor.
245 1 0 _aA1-Algebraic Topology over a Field
_h[electronic resource] /
_cby Fabien Morel.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2012.
300 _aX, 259 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2052
505 0 _a1 Introduction -- 2 Unramified sheaves and strongly A1-invariant sheaves -- 3 Unramified Milnor-Witt K-theories -- 4 Geometric versus canonical transfers -- 5 The Rost-Schmid complex of a strongly A1-invariant sheaf -- 6 A1-homotopy sheaves and A1-homology sheaves -- 7 A1-coverings -- 8 A1-homotopy and algebraic vector bundles -- 9 The affine B.G. property for the linear groups and the Grassmanian.
520 _aThis text deals with A<sup>1</sup>-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A<sup>1</sup>-homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to the properties and computations of A<sup>1</sup>-homotopy sheaves, A<sup>1</sup>-homotogy sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties.
650 0 _aMathematics.
650 0 _aGeometry, algebraic.
650 0 _aK-theory.
650 0 _aAlgebraic topology.
650 1 4 _aMathematics.
650 2 4 _aAlgebraic Geometry.
650 2 4 _aK-Theory.
650 2 4 _aAlgebraic Topology.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642295133
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2052
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-29514-0
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c103046
_d103046