Homology, Homotopy and Applications
Volume 17 (2015)
Motivic strict ring spectra representing semi-topological cohomology theories
Pages: 107 – 135
We show that Shipley’s “detection functor” for symmetric spectra generalizes to motivic symmetric spectra. As an application, we construct motivic strict ring spectra representing morphic cohomology, semi-topological $K$-theory, and semitopological cobordism for complex varieties. As a further application to semi-topological cobordism, we show that it is related to semi-topological $K$-theory via a Conner–Floyd type isomorphism and that after inverting a lift of the Friedlander–Mazur $s$-element in morphic cohomology, semi-topological cobordism becomes isomorphic to periodic complex cobordism.
motivic homotopy theory, semi-stable symmetric motivic spectra, semi-topological cohomology theory
2010 Mathematics Subject Classification
Primary 14F42, 14F43. Secondary 14C35, 19E15.