03184nam 22006135 450 991048400700332120200703145004.03-642-29514-210.1007/978-3-642-29514-0(CKB)3400000000085870(SSID)ssj0000745792(PQKBManifestationID)11412846(PQKBTitleCode)TC0000745792(PQKBWorkID)10852520(PQKB)10320781(DE-He213)978-3-642-29514-0(MiAaPQ)EBC3070573(PPN)165104368(EXLCZ)99340000000008587020120712d2012 u| 0engurnn|008mamaatxtccrA1-Algebraic Topology over a Field[electronic resource] /by Fabien Morel1st ed. 2012.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2012.1 online resource (X, 259 p.) Lecture Notes in Mathematics,0075-8434 ;2052Bibliographic Level Mode of Issuance: Monograph3-642-29513-4 Includes bibliographical references (p. 255-258) and index.1 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.This 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.Lecture Notes in Mathematics,0075-8434 ;2052Algebraic geometryK-theoryAlgebraic topologyAlgebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019K-Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11086Algebraic Topologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M28019Algebraic geometry.K-theory.Algebraic topology.Algebraic Geometry.K-Theory.Algebraic Topology.516.35Morel Fabienauthttp://id.loc.gov/vocabulary/relators/aut477681BOOK9910484007003321A1-algebraic topology over a field241165UNINA