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Pré-Publication, Document De Travail Année : 2023

On the injectivity and non-injectivity of the $l$-adic cycle class maps

Résumé

We study the injectivity of the cycle class map with values in Jannsen's continuous \'etale cohomology, by using refinements that go through \'etale motivic cohomology and the ``tame'' version of Jannsen's cohomology. In particular, we use this to show that the Tate and the Beilinson conjectures imply that its kernel is torsion in positive characteristic, and to revisit recent counterexamples to injectivity.

Dates et versions

hal-04306638 , version 1 (25-11-2023)

Identifiants

Citer

Bruno Kahn. On the injectivity and non-injectivity of the $l$-adic cycle class maps. 2023. ⟨hal-04306638⟩
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