Details
| Original language | English |
|---|---|
| Publication status | E-pub ahead of print - 12 Oct 2020 |
Abstract
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2020.
Research output: Working paper/Preprint › Preprint
}
TY - UNPB
T1 - Refined unramified homology of schemes
AU - Schreieder, Stefan
PY - 2020/10/12
Y1 - 2020/10/12
N2 - We introduce refined unramified cohomology groups. This notion allows us to give in arbitrary degree a cohomological interpretation of the failure of integral Hodge- or Tate-type conjectures, of l-adic Griffiths groups, and of the subgroup of the Griffiths group that consists of torsion classes with trivial transcendental Abel--Jacobi invariant. Our approach simplifies and generalizes to cycles of arbitrary codimension previous results of Bloch--Ogus, Colliot-Th\'el\`ene--Voisin, Voisin, and Ma that concerned cycles of low (co-)dimension. As an application, we give for any i>2 the first example of a uniruled smooth complex projective variety for which the integral Hodge conjecture fails for codimension i-cycles in a way that cannot be explained by the failure on any lower-dimensional variety.
AB - We introduce refined unramified cohomology groups. This notion allows us to give in arbitrary degree a cohomological interpretation of the failure of integral Hodge- or Tate-type conjectures, of l-adic Griffiths groups, and of the subgroup of the Griffiths group that consists of torsion classes with trivial transcendental Abel--Jacobi invariant. Our approach simplifies and generalizes to cycles of arbitrary codimension previous results of Bloch--Ogus, Colliot-Th\'el\`ene--Voisin, Voisin, and Ma that concerned cycles of low (co-)dimension. As an application, we give for any i>2 the first example of a uniruled smooth complex projective variety for which the integral Hodge conjecture fails for codimension i-cycles in a way that cannot be explained by the failure on any lower-dimensional variety.
M3 - Preprint
BT - Refined unramified homology of schemes
ER -