Unramified cohomology, integral coniveau filtration and Griffiths group
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Publication:6350208
DOI10.2140/AKT.2022.7.223zbMATH Open1507.14009arXiv2009.14447WikidataQ114045596 ScholiaQ114045596MaRDI QIDQ6350208
Publication date: 30 September 2020
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.
Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) (14F43) Algebraic cycles (14C25) (Equivariant) Chow groups and rings; motives (14C15)
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