A1-Algebraic Topology over a Field

• Main Author: Morel, Fabien (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012.
• Series: Lecture Notes in Mathematics, 2052
• Subjects: Mathematics.; Algebraic geometry.; K-theory.; Algebraic topology.; Algebraic Geometry.; K-Theory.; Algebraic Topology.
• Physical Description: X, 259 p. online resource.
• ISBN: 9783642295140
• ISSN: 0075-8434 ;

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.