For a smooth projective variety X over an algebraically closed field k, the group of indecomposable (2,1)-cycles on X is the quotient of H1 (X; K2) by the tensor product of Pic(X) with k*. We shall relate this group to other invariants of X : its Brauer group, the transcendental part of its motive (when dimX = 2) and its birational motivic cohomology.