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

Abstract

In this paper we show that the ℓn-torsion part of the cohomological Brauer groups of certain schemes associated to symmetric powers of a projective smooth curve over a separably closed field k are isomorphic, when ℓ is invertible in k. The schemes considered are the Symmetric powers themselves, then the corresponding Picard schemes and also certain Quot-schemes. We also obtain similar results for Prym varieties associated to certain finite covers of such curves.