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 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.
Domaines
Mathématiques [math]| Origine | Fichiers produits par l'(les) auteur(s) |
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