CMI Library

Your cart is empty.
Normal view MARC view ISBD view

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--

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--