Torsion models for tensor-triangulated categories: the one-step case

Given a suitable stable monoidal model category C and a specialization closed subset V of its Balmer spectrum, one can produce a Tate square for decomposing objects into the part supported over V and the part supported over Vc spliced with the Tate object. Using this one can show that C is Quillen equivalent to a model built from the data of local torsion objects, and the splicing data lies in a rather rich category. As an application, we promote the torsion model for the homotopy category of rational circle-equivariant spectra of Greenlees (1999) to a Quillen equivalence. In addition, a close analysis of the one-step case highlights important features needed for general torsion models, which we will return to in future work.