Filtrations via tensor actions

Greg Stevenson

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arXiv · 1206.2721

Filtrations via tensor actions

Greg Stevenson

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Abstract

We extend work of Balmer, associating filtrations of essentially small tensor triangulated categories to certain dimension functions, to the setting of actions of rigidly-compactly generated tensor triangulated categories on compactly generated triangulated categories. We show that the towers of triangles associated to such a filtration can be used to produce filtrations of Gorenstein injective quasi-coherent sheaves on Gorenstein schemes. This extends and gives a new proof of a result of Enochs and Huang. In the case of local complete intersections a further refinement of this filtration is given and we comment on some special properties of the associated spectral sequence in this case.

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Greg Stevenson. 2012-06-13. Filtrations via tensor actions. https://arxiv.org/abs/1206.2721

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