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A Gabriel Theorem for Coherent Twisted Sheaves

Arvid Perego
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Abstract

We give a generalization of Gabriel's Theorem on coherent sheaves to the case of coherent twisted sheaves on a smooth variety X over a field k. We show that the category Coh(X,\alpha) determines the scheme structure of X for \alpha in the Brauer group of X, and that any equivalence between Coh(X,\alpha) and Coh(Y,\beta) induces an isomorphism between X and Y. In conclusion we prove the saturatedness of D^b(X,\alpha).

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Arvid Perego. 2006-07-01. A Gabriel Theorem for Coherent Twisted Sheaves. https://arxiv.org/abs/math/0607025

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