Twisted Chern classes and -gerbes

Abstract: Using the language of stacks one can give a simple definition of functorial Chern classes for twisted sheaves. Calculating the cohomology ring of a -gerbe we observe that the twisted Chern classes used by Huybrechts and Stellari are specializations of these classes. We describe explicitly the relation between the choice of a cocycle in the definition of twisted sheaves and the 2-categorical structure of -gerbes. To cite this article: J. Heinloth, C. R. Acad. Sci. Paris, Ser. I 341 (2005). [Copyright &y& Elsevier]