Pré-Publication, Document De Travail Année : 2023

De Rham logarithmic classes and Tate conjecture

Résumé

We introduce the definition of De Rham logarithmic classes. We show that the De Rham class of an algebraic cycle of a smooth algebraic variety over a field of characteristic zero is logarithmic and conversely that a logarithmic class of bidegree (d, d) is the De Rham class of an algebraic cycle (of codimension d). We deduce from a previous work the Tate conjecture for smooth projective varieties over fields of finite type over Q, over p-adic fields for $\mathbb Q_p$ coefficients, p being a prime number.

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Dates et versions

hal-04034328 , version 1 (17-03-2023)
hal-04034328 , version 2 (03-04-2023)
hal-04034328 , version 3 (24-04-2023)
hal-04034328 , version 4 (18-05-2023)
hal-04034328 , version 5 (04-06-2023)
hal-04034328 , version 6 (19-06-2023)
hal-04034328 , version 7 (18-07-2023)
hal-04034328 , version 8 (06-08-2023)
hal-04034328 , version 9 (01-09-2023)
hal-04034328 , version 10 (12-09-2023)
hal-04034328 , version 11 (19-11-2023)
hal-04034328 , version 12 (24-09-2024)
hal-04034328 , version 13 (11-11-2024)
hal-04034328 , version 14 (13-02-2025)
hal-04034328 , version 15 (06-03-2025)
hal-04034328 , version 16 (12-09-2025)
hal-04034328 , version 17 (03-11-2025)
hal-04034328 , version 18 (19-11-2025)
hal-04034328 , version 19 (24-11-2025)
hal-04034328 , version 20 (09-12-2025)
hal-04034328 , version 21 (17-12-2025)
hal-04034328 , version 22 (07-01-2026)
hal-04034328 , version 23 (22-02-2026)
hal-04034328 , version 24 (01-03-2026)
hal-04034328 , version 25 (11-03-2026)
hal-04034328 , version 26 (23-03-2026)

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Identifiants

  • HAL Id : hal-04034328 , version 7

Citer

Johann Bouali. De Rham logarithmic classes and Tate conjecture. 2023. ⟨hal-04034328v7⟩
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