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 for
on the covering Ui 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 (Lieblich 2007).
This algebraic geometry–related article is a stub.