A1-Algebraic Topology over a Field [electronic resource] /by Fabien Morel.
by Morel, Fabien [author.]; SpringerLink (Online service).
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BookSeries: Lecture Notes in Mathematics: 2052Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : 2012.Description: X, 259 p. online resource.ISBN: 9783642295140.Subject(s): Mathematics | Geometry, algebraic | K-theory | Algebraic topology | Mathematics | Algebraic Geometry | K-Theory | Algebraic TopologyDDC classification: 516.35 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
| MAIN LIBRARY | QA564-609 (Browse shelf) | Available |
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| HB1-846.8 Global Analysis of Dynamic Models in Economics and Finance | TA357-359 Infrared Thermography for Thermo-Fluid-Dynamics | QA401-425 Quantum Many Body Systems | QA564-609 A1-Algebraic Topology over a Field | TA405-409.3 Green's Functions and Finite Elements | QH573-671 Intellectual Property Issues | TA349-359 Numerical Analysis of Vibrations of Structures under Moving Inertial Load |
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-homotogy sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties.
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