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A1-algebraic topology over a field / LNM 2052 Fabien Morel.

By: Morel, Fabien.
Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag): 2052.Publisher: Heidelberg ; New York : Springer, c2012Description: x, 259 p., E 44.95 ill. ; 23 cm.ISBN: 9783642295133 (pbk. : alk. paper); 3642295134 (pbk. : alk. paper).Other title: A.Subject(s): Algebraic topology | Homotopy theory
Contents:
Introduction -- Unramified sheaves and strongly Ap1s-invariant sheaves -- Unramified Milnor-Witt K-theories -- Geometric versus canonical transfers -- The Rost-Schmid complex of a strongly Ap1s-invariant sheaf -- Ap1s-homotopy sheaves and Ap1s-homology sheaves -- Ap1s-coverings, [Pi]Ap1s1 (Pn) and [Pi]Ap1s1 (SLn) -- Ap1s-homotopy and algebraic vector bundles -- The affine B.G. property for the linear groups and the Grassmanian -- The (Affine) B.G. property for simplicial sheaves -- Recollection on obstruction theory.
Summary: This text deals with Ap1s-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 Ap1s-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 Ap1s-homotopy sheaves, Ap1s-homotogy sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties--
Item type Current location Call number Status Date due Barcode Item holds
Book Chennai Mathematical Institute
General Stacks 		LNM (Browse shelf) Available 9246
Book Chennai Mathematical Institute
General Stacks 		LNM (Browse shelf) Available 8935
Total holds: 0

Includes bibliographical references (p. 255-258) and index.

Introduction -- Unramified sheaves and strongly Ap1s-invariant sheaves -- Unramified Milnor-Witt K-theories -- Geometric versus canonical transfers -- The Rost-Schmid complex of a strongly Ap1s-invariant sheaf -- Ap1s-homotopy sheaves and Ap1s-homology sheaves -- Ap1s-coverings, [Pi]Ap1s1 (Pn) and [Pi]Ap1s1 (SLn) -- Ap1s-homotopy and algebraic vector bundles -- The affine B.G. property for the linear groups and the Grassmanian -- The (Affine) B.G. property for simplicial sheaves -- Recollection on obstruction theory.

This text deals with Ap1s-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 Ap1s-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 Ap1s-homotopy sheaves, Ap1s-homotogy sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties--