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Twisted sheaf

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In mathematics, a twisted sheaf is a variant of a coherent sheaf. Precisely, it is specified by: an open covering in the étale topology Ui, coherent sheaves Fi over Ui, a Čech 2-cocycle θ on the covering Ui as well as the isomorphisms

satisfying

  • ,

The notion of twisted sheaves was introduced by Giraud. The above definition due to Căldăraru is down-to-earth but is equivalent to a more sophisticated definition in terms of gerbe; see § 2.1.3 of (Lieblich 2007).

See also

References

  • Căldăraru, A.: Derived categories of twisted sheaves on Calabi-Yau manifolds. Thesis, Cornell Univ., May 2000.
  • Lieblich, M.: Moduli of twisted sheaves, Duke Math. J. 138 (2007), no. 1, 23–118.