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020 a| 3642295134 (pbk. : alk. paper);

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100 1 a| Morel, Fabien.=| ^A703080;

245 10 a| A1-algebraic topology over a fieldh| [electronic resource] /c| Fabien Morel.;

246 3 a| A1-algebraic topology over a field;

260 a| Heidelberg ;a| New York :b| Springer,;

300 a| x, 259 p. :b| ill. ;c| 23 cm.;

490 1 a| Lecture notes in mathematics ;v| 2052;

504 a| Includes bibliographical references (p. 255-258) and index.;

505 0 a| Introduction -- Unramified sheaves and strongly A1-invariant sheaves -- Unramified Milnor-Witt K-theories -- Geometric versus canonical transfers -- The Rost-Schmid complex of a strongly A1-invariant sheaf -- A1-homotopy sheaves and A1-homology sheaves -- A1-coverings, [Pi]A11 (Pn) and [Pi]A11 (SLn) -- A1-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.;

506 a| Available only to authorized users.;

520 a| 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--c| Source other than Library of Congress.;

538 a| Mode of access: World Wide Web;

650 0 a| Algebraic topology.=| ^A22632;

650 0 a| Homotopy theory.=| ^A18132;

655 0 a| Electronic books.=| ^A491897;

830 0 a| Lecture notes in mathematics (Springer-Verlag) ;v| 2052.=| ^A496146;

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856 40 z| Full text available from Springer Booksu| https://go.openathens.net/redirector/ecu.edu?url=https%3A%2F%2Flink.springer.com%2F10.1007%2F978-3-642-29514-0;

856 40 z| Full text available from Springer Nature - Springer Mathematics and Statistics eBooks 2012 English Internationalu| https://go.openathens.net/redirector/ecu.edu?url=https%3A%2F%2Flink.springer.com%2F10.1007%2F978-3-642-29514-0;

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A1-algebraic topology over a field / Fabien Morel.

Author/creator	Morel, Fabien
Format	Electronic
Publication Info	Heidelberg ; New York : Springer,
Description	x, 259 p. : ill. ; 23 cm.
Supplemental Content	Full text available from SpringerLINK Lecture Notes in Mathematics Contemporary (1997-present)
Supplemental Content	Full text available from Springer Books
Supplemental Content	Full text available from Springer Nature - Springer Mathematics and Statistics eBooks 2012 English International
Subjects	Algebraic topology. Homotopy theory.

Variant title	A1-algebraic topology over a field
Series	Lecture notes in mathematics ; 2052 Lecture notes in mathematics (Springer-Verlag) ; 2052. ^A496146
Contents	Introduction -- Unramified sheaves and strongly A1-invariant sheaves -- Unramified Milnor-Witt K-theories -- Geometric versus canonical transfers -- The Rost-Schmid complex of a strongly A1-invariant sheaf -- A1-homotopy sheaves and A1-homology sheaves -- A1-coverings, [Pi]A11 (Pn) and [Pi]A11 (SLn) -- A1-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.
Abstract	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-- Source other than Library of Congress.
Bibliography note	Includes bibliographical references (p. 255-258) and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2012942079
ISBN	9783642295133 (pbk. : alk. paper)
ISBN	3642295134 (pbk. : alk. paper)

A1-algebraic topology over a field / Fabien Morel.

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