论文标题
过滤对象和滑轮的张量三角几何形状
Tensor triangular geometry of filtered objects and sheaves
论文作者
论文摘要
我们计算了张量三角类别的紧凑对象的Balmer光谱，其对象被过滤或分级的对象（或重新值）的另一个张量三角类别。值得注意的示例包括方案的过滤派生类别以及过滤光谱的同型类别。我们使用$ \ infty $ - 类别方法来正确制定和处理该问题。我们的计算基于一种无点的方法，因此将分布式格子和半层次用作关键工具。 在附录中，我们证明，$ \ infty $ topos在$ \ infty $ site上的$ \ infty $ topos是从基础上回收的，这可能是独立的。
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.
