دانلود کتاب A1-algebraic topology over a field

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. Read more... Introduction -- Background -- Materials and Methods -- Results and Discussions -- Conclusion. Unramified Sheaves and Strongly mathbbA1A1-Invariant Sheaves -- Unramified Milnor-Witt K-Theories -- Geometric Versus Canonical Transfers -- The Rost-Schmid Complex of a Strongly mathbbA1A1-Invariant Sheaf -- mathbbA1A1-Homotopy Sheaves and mathbbA1A1-Homology Sheaves -- mathbbA1A1-Coverings, p1mathbbA1 (mathbbPn)1A1(Pn) and p1mathbbA1 (SLn)1A1(SLn) -- mathbbA1A1-Homotopy and Algebraic Vector Bundles -- The Affine B.G. Property for the Linear Groups and the Grassmanian