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    Title      l  Semi-topologization in motivic homotopy theory and applications
    Author   l  Amalendu Krishna and Jinhyun Park 
    Date   l  2013-09-30
    Category   l  ASARC-Prepint-13-07
    Download    l 1380504956_0.184371.pdf  
Abstract. In this paper, we study semi-topological cohomology theories such as semitopological
K-theory and morphic cohomology from the perspective of the motivic
homotopy theory. Using some motivic descent theorems for Morels A1-B.G. motivic
spectra, we construct a triangulated endo-functor on the stable motivic homotopy
category SH(C), which we call homotopy semi-topologization.
Using this functor we show that the semi-topological K-theory of Friedlander-Walker
and the morphic cohomology of Friedlander-Lawson are representable in SH(C). The
homotopy semi-topologization functor allows us to de ne a semi-topological analogue
of the algebraic cobordism of Voevodsky. We show that there is a Hopkins-Morel type
spectral sequence, which relates the morphic cohomology with the semi-topological
cobordism, and this spectral sequence degenerates with the rational coecients. We
also show that the Voevodsky algebraic cobordism coincides with the semi-topological
cobordism with nite coecients.

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