Brauer groups of tame stacky curves and their ${\mu }_r$-gerbes

Abstract

We fit the Brauer group of a ${\mu }_r$-gerbe over a (possibly arbitrarily singular) stacky curve into an exact sequence and give characterizations for when it is short exact and conditions for when it splits. We also give a precise formula for the Brauer group of a ${\mu }_r$-gerbe in the case that the base curve is smooth.

24 pages. Rewrote intro, reorganized background, removed extraneous result, mild improvements throughout