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

Part of: $K$-theory in geometry (Co)homology theory

Published online by Cambridge University Press:  17 December 2015

Bruno Kahn
Bruno Kahn*
Affiliation:
IMJ-PRG, Case 247, 4 place Jussieu, 75252 Paris Cedex 05, France email bruno.kahn@imj-prg.fr
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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 $b_{2}-{\it\rho}>0$. We derive a new insight into Roǐtman’s theorem on torsion $0$-cycles over a surface.

Keywords

motivic cohomologyBrauer groupRoǐtman’s theorem

MSC classification

Primary: 19E15: Algebraic cycles and motivic cohomology 14F22: Brauer groups of schemes
Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 5 , May 2016 , pp. 1041 - 1051
Copyright
© The Author 2015 

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