A1-Algebraic Topology over a Field

  • Fabien Morel

Part of the Lecture Notes in Mathematics book series (LNM, volume 2052)

About this book


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.


14-XX; 19-XX; 55-XX Algebraic vector bundles Milnor-Witt K-theory Motivic homotopy theory Sheaves with transfers

Authors and affiliations

  • Fabien Morel
    • 1
  1. 1.Institut für MathematikUniversität MünchenMünchenGermany

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