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arXiv · 2009.14447

Unramified cohomology, integral coniveau filtration and Griffiths group

Shouhei Ma
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Abstract

We prove that the degree k unramified cohomology with torsion coefficients of a smooth complex projective variety X with small CH_0(X) has a filtration of length [k/2], whose first piece is the torsion part of the quotient of the degree k+1 integral singular cohomology by its coniveau 2 subgroup, and whose next graded piece is controlled by the Griffiths group Griff^{k/2+1}(X) when k is even and is related to the higher Chow group CH^{(k+3)/2}(X, 1) when k is odd. The first piece is a generalization of the Artin-Mumford invariant (k=2) and the Colliot-Thelene-Voisin invariant (k=3). We also give an analogous result for certain H-cohomology groups.

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Shouhei Ma. 2020-09-30. Unramified cohomology, integral coniveau filtration and Griffiths group. https://arxiv.org/abs/2009.14447

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