Unramified cohomology, integral coniveau filtration and Griffiths group

2020/09/30 by Ma, Shouhei
#14C15 #14C25 #14F43 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.14447

Abstract

We prove that the degree k unramified cohomology with torsion coefficients of a smooth complex projective variety X with small CH₀(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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