We give a list of statements on the geometry of elliptic threefolds phrased only in the language of topology and homological algebra. Using only notions from topology and homological algebra, we recover existing results and prove new results on torsion pairs in the category of coherent sheaves on an elliptic threefold.

中文翻译：

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椭圆三折上的扭转理论计算框架

我们给出了仅用拓扑和同调代数语言表达的关于椭圆三重几何的陈述列表。仅使用拓扑和同调代数中的概念，我们恢复了现有结果并证明了椭圆三重上相干滑轮类别中扭转对的新结果。