A[1]-algebraic topology over a field
著者
書誌事項
A[1]-algebraic topology over a field
（Lecture notes in mathematics, 2052）
Springer, c2012
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注記
[1] is superscript
Includes bibliographical references (p. 255-258) and index
内容説明・目次
内容説明
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.
目次
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
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