Homology, Homotopy and Applications

Volume 17 (2015)

Number 2

Motivic strict ring spectra representing semi-topological cohomology theories

Pages: 107 – 135

DOI: https://dx.doi.org/10.4310/HHA.2015.v17.n2.a7

Author

Jeremiah Heller (Department of Mathematics, University of Illinois, Urbana, Il., U.S.A.)

Abstract

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.

Keywords

motivic homotopy theory, semi-stable symmetric motivic spectra, semi-topological cohomology theory

2010 Mathematics Subject Classification

Primary 14F42, 14F43. Secondary 14C35, 19E15.

Published 3 December 2015