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arXiv · 1401.0791

The Brauer group and indecomposable (2,1)-cycles

Bruno Kahn
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Abstract

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 $b_2-\rho>0$. We derive a new insight into Roitman's theorem on torsion $0$-cycles over a surface.

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Bruno Kahn. 2014-01-04. The Brauer group and indecomposable (2,1)-cycles. https://doi.org/10.1112/s0010437x15007733

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