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2 results

  • Model structures for pro-simplicial presheaves

  • J.F. Jardine
  • Journal:
    Journal of K-Theory / Volume 7 / Issue 3 / June 2011
    Published online by Cambridge University Press:
    24 May 2011, pp. 499-525
    Print publication:
    June 2011

  • This paper displays model structures for the category of pro-objects in simplicial presheaves on an arbitrary small Grothendieck site. The first of these is an analogue of the Edwards-Hastings model structure for pro-simplicial sets, in which the cofibrations are monomorphisms and the weak equivalences are specified by comparisons of function complexes. Other model structures are built from the Edwards-Hastings structure by using Bousfield-Friedlander localization techniques. There is, in particular, an n-type structure for pro-simplicial presheaves, and also a model structure in which the map from a pro-object to its Postnikov tower is formally inverted.

  • Rationally trivial torsors in -homotopy theory

  • Matthias Wendt
  • Journal:
    Journal of K-Theory / Volume 7 / Issue 3 / June 2011
    Published online by Cambridge University Press:
    16 May 2011, pp. 541-572
    Print publication:
    June 2011

  • In this paper, we show that rationally trivial torsors under split smooth linear algebraic groups induce fibre sequences in -homotopy theory. The results allow geometric proofs of stabilization results for unstable Karoubi-Villamayor K-theories and a description of the second -homotopy group of the projective line.