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arXiv · 1806.00078

Compactly generated t-structures in the derived category of a commutative ring

Michal Hrbek
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Abstract

We classify all compactly generated t-structures in the unbounded derived category of an arbitrary commutative ring, generalizing the result of [ATLJS10] for noetherian rings. More specifically, we establish a bijective correspondence between the compactly generated t-structures and infinite filtrations of the Zariski spectrum by Thomason subsets. Moreover, we show that in the case of a commutative noetherian ring, any bounded below homotopically smashing t-structure is compactly generated. As a consequence, all cosilting complexes are classified up to equivalence.

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Michal Hrbek. 2018-05-31. Compactly generated t-structures in the derived category of a commutative ring. https://arxiv.org/abs/1806.00078

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