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Preprints, Working Papers, ... Year : 2023

De Rham logarithmic classes and Tate conjecture

Abstract

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 also give for smooth algebraic varieties over a $p$-adic field an analytic version of this result. We deduce from the analytical case 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 and 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)

Identifiers

  • HAL Id : hal-04034328 , version 10

Cite

Johann Bouali. De Rham logarithmic classes and Tate conjecture. 2023. ⟨hal-04034328v10⟩
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