标题： 支持情况下的重构定理 显示英文标题

标题： Reconstruction theorems in the supported case

摘要： 我们证明了在两个情况下，任何在光滑射影复流形上凝聚层的有界导出范畴之间的等价关系，其支持在一个闭代数子集上，会保持支持的维数：(i) 支持上（反）规范丛的限制是充分大的；(ii) 支持是不可约的，并且该等价关系将一个闭点的天际层映射为一个闭点的天际层。 此外，在第一种情况下，该等价关系可以恢复支持的闭点集合，同胚意义下。 显示英文摘要

摘要： We show that any equivalence of bounded derived categories of coherent sheaves on a smooth projective complex variety supported in a closed algebraic subset preserves the dimension of the support in two cases: (i) the restriction of the (anti)canonical bundle to the support is ample; (ii) the supports are irreducible and the equivalence sends a skyscraper sheaf of a closed point to a skyscraper sheaf of a closed point. Moreover, in the first case the equivalence recovers the set of closed points of the support up to homeomorphism.