论文标题
倾斜复合物的拓扑内态环
Topological endomorphism rings of tilting complexes
论文作者
论文摘要
在紧凑的三角类别中，我们引入了满足某些纯度条件的一类倾斜对象。我们将这些称为体面的倾斜物体，并表明任何此类物体引起的倾斜心脏相当于倾斜物体的内态态环上的一类构造，并具有天然的线性拓扑结构。这扩展了Positselki和šťovíček的N倾斜模块的最新结果。在一个环上的模块的派生类别的环境中，我们表明，体面的倾斜复合物恰好是磨碎的复合物，使它们的特征双重二极管在启动。相对于同一拓扑环，辅助型类型的辅助复合物的心脏相当于离散模块的类别。最后，在这种情况下，我们提供了一种莫里塔理论：体面的倾斜络合物对应于由倾斜和引导得出的对等对应的对，如上所述，与张量的兼容性条件相关。
In a compactly generated triangulated category, we introduce a class of tilting objects satisfying certain purity condition. We call these the decent tilting objects and show that the tilting heart induced by any such object is equivalent to a category of contramodules over the endomorphism ring of the tilting object endowed with a natural linear topology. This extends the recent result for n-tilting modules by Positselski and Šťovíček. In the setting of the derived category of modules over a ring, we show that the decent tilting complexes are precisely the silting complexes such that their character dual is cotilting. The hearts of cotilting complexes of cofinite type turn out to be equivalent to the category of discrete modules with respect to the same topological ring. Finally, we provide a kind of Morita theory in this setting: Decent tilting complexes correspond to pairs consisting of a tilting and a cotilting derived equivalence as described above tied together by a tensor compatibility condition.
