Algebraic Geometry Seminar: On the decomposition of etale gerbes

Let G be a finite group. A G-gerbe over a space X may be intuitively thought of as a fiber bundle over X with fibers being the classifying space (stack) BG. In particular BG itself is the G-gerbe over a point. A more interesting class of examples consist of G-gerbes over BQ, which are equivalent to extensions of the finite group Q by G.

Considerations from physics have led to conjectures asserting that the geometry of a G-gerbe Y over X is equivalent to certain "twisted" geometry of a "dual" space Y'. A lot of progresses have be made recently towards proving these conjectures in general. In this talk we'll try to explain these conjectures in the elementary concrete examples of G-gerbes over a point or BQ.