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A¹-algebraic topology over a field / Fabien Morel.

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Author/Creator:
Morel, Fabien.
Language:
English.
Publication date:
2012
Imprint:
Heidelberg ; New York : Springer, c2012.
Format:
  • Book
  • x, 259 p. : ill ; 23 cm.
Title Variation:
A1-algebraic topology over a field
Bibliography:
Includes bibliographical references (p. 255-258) and index.
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.
Summary:
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.
Series:
Lecture notes in mathematics ; 2052
Lecture notes in mathematics (Springer-Verlag) ; 2052.
Subjects:
ISBN:
9783642295133
3642295134

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