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Adelic models for Noetherian model categories (joint work with John Greenlees)

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HHH - Homotopy harnessing higher structures

The algebraic models for rational G-equivariant cohomology theories (Barnes, Greenlees, Kedziorek, Shipley) are constructed by assembling data from each closed subgroup of G. We can compare this to the usual Hasse square, where we see abelian groups being constructed from data at each point of Spec(Z) in an adelic fashion.   This style of assembly can be described in a general fashion using the data contained in the Balmer spectrum of the corresponding tensor-triangulated categories. We show that given a Quillen model category whose homotopy category is a suitably well behaved tensor-triangulated category, that we can construct a Quillen equivalent model from localized p-complete data at each Balmer prime in an adelic fashion.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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