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Mathematics, Algebraic Topology, Commutative Algebra, Category Theory
Abstract:
Given a suitable stable monoidal model category $\mathscr{C}$ 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 $V^c$ spliced with the Tate object. Using this one can show that
$\mathscr{C}$ 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 from [18] 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.
