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

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.

Final version, to appear in Compositio Math

Cited by in corpus (3)

• Motivic periods and Grothendieck arithmetic invariants
• Divisibility properties of motivic cohomology
• Albanese kernels and Griffiths groups