Group actions on stacks -- Behrang Noohi, March 7, 2008

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We begin with a general discussion of difficulties arising
in formulating group action problems on stacks. We then cast these
in a homotopy theoretic language and propose a machinery which
invokes the theory of crossed modules and butterflies to systematically
study actions of (2-)group schemes on stacks.  As an application, we
explain how this method was used (in joint work with Kai Behrend)
to classify smooth Deligne-Mumford curves.