Year: 2025
Type: article
Abstract: We extend the basic theory of the coniveau and strong coniveau filtrations to the ℓ-adic setting.By adapting the examples of Benoist-Ottem to the ℓ-adic context, we show that the two filtrations differ over any algebraically closed field of characteristic not 2. When the base field F is finite, we show that the equality of the two filtrations over the algebraic closure F has some consequences for algebraic equivalence for codimension 2 cycles over F. As an application, we prove that the third unramified cohomology group H 3 nr (X, Q ℓ /Z ℓ ) vanishes for a large class of rationally chain-connected threefolds X over F, confirming a conjecture of Colliot-Thélène and Kahn.
Source: Algebraic geometry
DOI: 10.14231/ag-2025-019
Authors: Federico Scavia, Fumiaki Suzuki
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413468532