A Gabriel Theorem for Coherent Twisted Sheaves
Algebraic Geometry
2014-03-04 v2
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).
Cite
@article{arxiv.math/0607025,
title = {A Gabriel Theorem for Coherent Twisted Sheaves},
author = {Arvid Perego},
journal= {arXiv preprint arXiv:math/0607025},
year = {2014}
}
Comments
21 pages, Added references