Positive model structures for abstract symmetric spectra

Details Positive model structures for abstract symmetric spectra Positive model structures for abstract symmetric spectra

2011-08-17

arxiv.org/abs/1108.3509v2

Mathematics

Algebraic Topology

24 pages

Scientific paper

We prove the existence of a suitable "positive" model structure for symmetric spectra over an abstract simplicial monoidal model category. This allows to generalize the theorem due to Elmendorf, Kriz, Mandell and May saying that the $n$-th symmetric power of a positively cofibrant topological spectrum is stably equivalent to the $n$-th homotopy symmetric power of that spectrum, see \cite{EKMM}, III, 5.1, and \cite{MMSS}, 15.5. As a consequence, we also prove the existence of left derive symmetric powers for abstract symmetric spectra. The results are general enough to be applicable to the Morel-Voevodsky's motivic symmetric spectra of schemes over a field.

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