Twisted sheaf

In mathematics, a twisted sheaf is a variant of a coherent sheaf. Precisely, it is specified by: an open covering in the étale topology "U""i", coherent sheaves "F""i" over "U""i", a Čech 2-cocycle "θ" on the covering "U""i" as well as the isomorphisms
satisfying
The notion of twisted sheaves was introduced by Jean 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 .