Adelic models of tensor-triangulated categories

We show that a well behaved Noetherian, finite dimensional, stable, monoidal model category has a model built from categories of modules over completed rings in an adelic fashion. Special cases include abelian groups (the Hasse square), chromatic homotopy theory (a module theoretic chromatic fractur...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2020-12, Vol.375, p.107339, Article 107339
Main Authors: Balchin, Scott, Greenlees, J.P.C.
Format: Article
Language:English
Subjects:
Adelic approximation
Algebraic model
Balmer spectrum
Completion
Localization
Tensor triangulated category
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Summary:We show that a well behaved Noetherian, finite dimensional, stable, monoidal model category has a model built from categories of modules over completed rings in an adelic fashion. Special cases include abelian groups (the Hasse square), chromatic homotopy theory (a module theoretic chromatic fracture square), and rational torus-equivariant homotopy theory (first step to the model of [30]).
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2020.107339