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Telescope conjecture for homotopically smashing t-structures over commutative noetherian rings
Journal of Pure and Applied Algebra ( IF 0.7 ) Pub Date : 2021-04-01 , DOI: 10.1016/j.jpaa.2020.106571
Michal Hrbek , Tsutomu Nakamura

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:

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。
更新日期:2021-04-01
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