Telescope conjecture for homotopically smashing t-structures over commutative noetherian rings

Abstract

We show that any homotopically smashing t-structure in the derived category of a commutative noetherian ring is compactly generated. This generalizes the validity of the telescope conjecture for commutative noetherian rings due to Neeman. As another consequence, we obtain a cofinite type result for pure-injective cosilting objects. We also give a formulation of telescope conjecture for homotopically smashing t-structures in underlying triangulated categories of certain Grothendieck derivators.

arXiv comment15 pages, minor revision, to appear in Journal of Pure and Applied Algebra

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Cited by in corpus (6)

• Hearts for commutative noetherian rings: torsion pairs and derived equivalences
• Tilting complexes and codimension functions over commutative noetherian rings
• Mutation and torsion pairs
• Gluing compactly generated t-structures over stalks of affine schemes
• Singular equivalences to locally coherent hearts of commutative noetherian rings
• Mutation and the Gabriel spectrum