Symmetric powers in stable homotopy categories

Details Symmetric powers in stable homotopy categories Symmetric powers in stable homotopy categories

2009-07-03

arxiv.org/abs/0907.0730v2

Mathematics

Algebraic Geometry

59 pages

Scientific paper

We construct Z-coefficient symmetric powers in a symmetric monoidal triangulated category, provided it is the homotopy category of a closed simplicial symmetric monoidal model category. Under certain natural assumptions, we show an existence of functorial towers for symmetric powers in distinguished triangles whose cones can be computed by Kuenneth's rule. Our theory is applicable to the topological and motivic stable homotopy categories through the idea of symmetric spectra. Some applications are presented and open questions are raised in both topological and motivic settings.

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