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arXiv · 1601.01205

The local-to-global principle for triangulated categories via dimension functions

Greg Stevenson
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Abstract

We formulate a general abstract criterion for verifying the local-to-global principle for a rigidly-compactly generated tensor triangulated category. Our approach is based upon an inductive construction using dimension functions. Using our criterion we give a new proof of the theorem that the local-to-global principle holds for such categories when they have a model and the spectrum of the compacts is noetherian. As further applications we give a new set of conditions on the spectrum of the compacts that guarantee the local-to-global principle holds and use this to classify localising subcategories in the derived category of a semi-artinian absolutely flat ring.

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Greg Stevenson. 2016-02-24. The local-to-global principle for triangulated categories via dimension functions. https://arxiv.org/abs/1601.01205

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