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Published online by Cambridge University Press: 17 December 2015
We show that the torsion in the group of indecomposable $(2,1)$-cycles on a smooth projective variety over an algebraically closed field is isomorphic to a twist of its Brauer group, away from the characteristic. In particular, this group is infinite as soon as
$b_{2}-{\it\rho}>0$. We derive a new insight into Roǐtman’s theorem on torsion
$0$-cycles over a surface.