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arXiv · 1304.6288

Motivic strict ring spectra representing semi-topological cohomology theories

Jeremiah Heller
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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 semi-topological 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.

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Jeremiah Heller. 2013-04-23. Motivic strict ring spectra representing semi-topological cohomology theories. https://arxiv.org/abs/1304.6288

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