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In this paper we show that the l^n-torsion part of the cohomological Brauergroups of certain schemes associated to symmetric powers of a projective smoothcurve over a separably closed field k are isomorphic, when `l is invertible ink. The schemes considered are the Symmetric powers themselves, then thecorresponding Picard schemes and also certain Quot-schemes. We also obtainsimilar results for Prym varieties associated to certain finite covers of suchcurves: we prove such results only for curves defined over the field of complexnumbers.

Brauer groups of schemes associated to symmetric powers of smooth projective curves in arbitrary characteristics