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arXiv · 2303.09932

De Rham logarithmic classes and Tate conjecture

Johann Bouali
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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 analytic case the Tate conjecture for smooth projective varieties over fields of finite type over $\mathbb Q$.

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Johann Bouali. 2023-03-17. De Rham logarithmic classes and Tate conjecture. https://arxiv.org/abs/2303.09932

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