滤过对象与层的张量三角几何
Tensor triangular geometry of filtered objects and sheaves
AI总结：
本文利用∞-范畴与无点方法，通过分配格和半格等工具计算了滤过或分次对象所成张量三角范畴中紧对象的 Balmer 谱，并应用于概形滤过导出范畴与滤过谱同伦范畴。
摘要：
我们计算了张量三角范畴中紧对象的 Balmer 谱，这些范畴的对象是另一个张量三角范畴的滤过对象或分次对象（或取值于其中的层）。值得注意的例子包括概形的滤过导出范畴以及滤过谱的同伦范畴。我们使用一种 ∞-范畴方法来恰当地表述和处理该问题。我们的计算基于一种无点方法，因此分配格和半格被用作关键工具。在附录中，我们证明了 ∞-位形上超完备层的 ∞-拓扑斯可由一个基恢复，这可能具有独立的意义。
英文摘要：
We compute the the Balmer spectra of compact objects of tensor triangulated categories whose objects are filtered or graded objects of (or sheaves valued in) another tensor triangulated category. Notable examples include the filtered derived category of a scheme as well as the homotopy category of filtered spectra. We use an $\infty$-categorical method to properly formulate and deal with the problem. Our computations are based on a point-free approach, so that distributive lattices and semilattices are used as key tools. In the appendix, we prove that the $\infty$-topos of hypercomplete sheaves on an $\infty$-site is recovered from a basis, which may be of independent interest.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
