De Rham logarithmic classes and Tate conjecture

Johann Bouali (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Domains: Mathematics [math]

Johann Bouali. De Rham logarithmic classes and Tate conjecture. 2023. ⟨hal-04034328v4⟩