A¹-algebraic topology over a field
- Fabien Morel.
- Heidelberg ; New York : Springer, c2012.
- Physical description
- x, 259 p. : ill ; 23 cm.
- Lecture notes in mathematics (Springer-Verlag) 2052.
Math & Statistics Library
|QA3 .L28 V.2052||Unknown|
- Morel, Fabien.
- Includes bibliographical references (p. 255-258) and index.
- 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.
- 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.
- Publication date
- Title Variation
- A1-algebraic topology over a field
- Lecture notes in mathematics ; 2052
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