A¹algebraic topology over a field
 Author/Creator
 Morel, Fabien.
 Language
 English.
 Imprint
 Heidelberg ; New York : Springer, c2012.
 Physical description
 x, 259 p. : ill ; 23 cm.
 Series
 Lecture notes in mathematics (SpringerVerlag) 2052.
Access
Available online

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QA3 .L28 V.2052

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QA3 .L28 V.2052
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 255258) and index.
 Contents

 Introduction
 Unramified sheaves and strongly A¹invariant sheaves
 Unramified MilnorWitt Ktheories
 Geometric versus canonical transfers
 The RostSchmid complex of a strongly A¹invariant sheaf
 A¹homotopy sheaves and A¹homology sheaves
 A¹coverings, [Pi]A¹1 (Pn) and [Pi]A¹1 (SLn)
 A¹homotopy 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 A¹homotopy 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 A¹homotopy 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 A¹homotopy sheaves, A¹homotogy sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties.
Subjects
Bibliographic information
 Publication date
 2012
 Responsibility
 Fabien Morel.
 Title Variation
 A1algebraic topology over a field
 Series
 Lecture notes in mathematics ; 2052
 ISBN
 9783642295133
 3642295134