A1-Algebraic Topology over a Field [electronic resource] /
Morel, Fabien.author.
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.
Bibliographic Level Mode of Issuance: Monograph
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.
Algebraic geometry.
K-theory.
Algebraic topology.
Algebraic Geometry.
K-Theory.
Algebraic Topology.