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A Gabriel Theorem for coherent twisted sheaves

机译:相干扭绳轮的加百利定理

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The aim of this work is to give a generalization of Gabriel's Theorem on coherent sheaves to coherent twisted sheaves on noetherian schemes. We start by showing that we can recover a noetherian scheme X from the category Coh(X, alpha) of coherent alpha-twisted sheaves over X, where alpha lies in the cohomological Brauer group of X. This follows from the bijective correspondence between closed subsets of X and Serre subcategories of finite type of Coh(X, alpha). Moreover, any equivalence between Coh(X, alpha) and Coh(Y, beta), where X and Y are noetherian schemes, and alpha is an element of Br' (X), beta Br' (Y) induces an isomorphism between X and Y.
机译:这项工作的目的是对相干绳轮上的加百列定理推广到noetherian方案上相干扭曲绳轮的推广。我们首先显示出,我们可以从X上相干的α扭曲滑轮的Coh(X,alpha)类别中恢复Noether方案X,其中α位于X的同色Brauer群中。这来自闭合子集之间的双射对应有限类型的Coh(X,alpha)的X和Serre子类别的集合。此外,Coh(X,alpha)和Coh(Y,beta)之间的任何等价关系(其中X和Y是noetherian方案,而alpha是Br'(X)的元素,βBr'(Y)会引起X之间的同构和Y。

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