1.

Record Nr.

UNISA996466770903316

Autore

Morel Fabien

Titolo

A1-Algebraic Topology over a Field [[electronic resource] /] / by Fabien Morel

Pubbl/distr/stampa

Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2012

ISBN

3-642-29514-2

Edizione

[1st ed. 2012.]

Descrizione fisica

1 online resource (X, 259 p.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 2052

Disciplina

516.35

Soggetti

Algebraic geometry

K-theory

Algebraic topology

Algebraic Geometry

K-Theory

Algebraic Topology

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

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

Nota di contenuto

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.

Sommario/riassunto

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.