{"product_id":"a1-algebraic-topology-over-a-field-9783642295133","title":"A1-Algebraic Topology over a Field","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis text deals with A\u003csup\u003e1\u003c\/sup\u003e-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\u003csup\u003e1\u003c\/sup\u003e-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\u003csup\u003e1\u003c\/sup\u003e-homotopy sheaves, A\u003csup\u003e1\u003c\/sup\u003e-homology sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e1 Introduction.- 2 Unramified sheaves and strongly A\u003csup\u003e1\u003c\/sup\u003e-invariant sheaves.- 3 Unramified Milnor-Witt K-theories.- 4 Geometric \u003ci\u003eversus\u003c\/i\u003e canonical transfers.- 5 The Rost-Schmid complex of a strongly A\u003csup\u003e1\u003c\/sup\u003e-invariant sheaf.- 6 A\u003csup\u003e1\u003c\/sup\u003e-homotopy sheaves and A\u003csup\u003e1\u003c\/sup\u003e-homology sheaves.- 7 A\u003csup\u003e1\u003c\/sup\u003e-coverings.- 8 A\u003csup\u003e1\u003c\/sup\u003e-homotopy and algebraic vector bundles.- 9 The affine B.G. property for the linear groups and the Grassmanian\u003c\/p\u003e","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":52091519730007,"sku":"9783642295133","price":47.49,"currency_code":"GBP","in_stock":false}],"url":"https:\/\/bookcurl.com\/products\/a1-algebraic-topology-over-a-field-9783642295133","provider":"Book Curl","version":"1.0","type":"link"}