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<sub>i</sub>, coherent sheaves F<sub>i</sub> over U<sub>i</sub>, a ÃÂech 2-cocycle ø for on the covering U<sub>i</sub> as well as the isomorphisms
satisfying
The notion of twisted sheaves was introduced by Jean Giraud. The above definition due to CÃÂldÃÂraru is down-to-earth but is equivalent to a more sophisticated definition in terms of gerbe; see ç 2.1.3 of .