LEADER 02653nam 2200553Ia 450 001 9910484007003321 005 20200520144314.0 010 $a3-642-29514-2 024 7 $a10.1007/978-3-642-29514-0 035 $a(CKB)3400000000085870 035 $a(SSID)ssj0000745792 035 $a(PQKBManifestationID)11412846 035 $a(PQKBTitleCode)TC0000745792 035 $a(PQKBWorkID)10852520 035 $a(PQKB)10320781 035 $a(DE-He213)978-3-642-29514-0 035 $a(MiAaPQ)EBC3070573 035 $a(PPN)165104368 035 $a(EXLCZ)993400000000085870 100 $a20120324d2012 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aA1-algebraic topology over a field /$fFabien Morel 205 $a1st ed. 2012. 210 $aBerlin ;$aHeidelberg $cSpringer$dc2012 215 $a1 online resource (X, 259 p.) 225 1 $aLecture notes in mathematics ;$v2052 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-29513-4 320 $aIncludes bibliographical references (p. 255-258) and index. 327 $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. 330 $aThis text deals with A1-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A1-homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to the properties and computations of A1-homotopy sheaves, A1-homology sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v2052. 606 $aAlgebraic topology 606 $aHomotopy theory 615 0$aAlgebraic topology. 615 0$aHomotopy theory. 676 $a514.24 700 $aMorel$b Fabien$0477681 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484007003321 996 $aA1-algebraic topology over a field$9241165 997 $aUNINA