Geometry and Arithmetic

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pp: 347–368

DOI: 10.4171/119-1/20

Degree 4 unramified cohomology with finite coefficients and torsion codimension 3 cycles

Claire Voisin[1]

(1) Coll├Ęge de France, Paris, France

We study in this paper degree $4$ unramified cohomology with torsion coefficients of a smooth projective variety $X$. We show that if $CH_0(X)$ is small, it is isomorphic to the group of torsion codimension $3$ cycles with trivial Deligne cycle class, modulo algebraic equivalence.

Keywords: Unramified cohomology, Griffiths group, Deligne cycle class