Abstract:Extending work of Meinhardt and Partsch, we prove that two varieties are isomorphic away from a subset of a given dimension if and only if certain quotients of their categories of coherent sheaves are equivalent. This result interpolates between Gabriel's reconstruction theorem and the fact that two varieties are birational if and only if they have the same function field.

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中文翻译：

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加布里埃尔定理和双边几何

摘要：扩展了Meinhardt和Partsch的工作，我们证明了，当且仅当相干滑轮类别中的某些商相等时，两个变种才与给定维度的子集同构。该结果在Gabriel的重构定理和两个变量具有且仅当它们具有相同的函数场时是双歧的这一事实之间进行插值。

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