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.