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.

中文翻译：

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可交换诺特环上同伦粉碎 t 结构的望远镜猜想

摘要 我们表明，可交换诺特环的派生类别中的任何同伦粉碎 t 结构都是紧凑生成的。这概括了由于尼曼引起的可交换诺特环的望远镜猜想的有效性。作为另一个结果，我们获得了纯注入共淤对象的余有限类型结果。我们还给出了望远镜猜想的公式，用于在某些 Grothendieck 导数的潜在三角化类别中同调粉碎 t 结构。