De Rham logarithmic classes and Tate conjecture - HAL UNIV-PARIS8 - open access Access content directly
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 an 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 and over field of characteristic p, p being a prime number.
Fichier principal
Vignette du fichier
LogTate4.pdf (178.89 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

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)
hal-04034328 , version 11 (19-11-2023)

Identifiers

  • HAL Id : hal-04034328 , version 1

Cite

Johann Bouali. De Rham logarithmic classes and Tate conjecture. 2023. ⟨hal-04034328v1⟩
343 View
37 Download

Share

Gmail Facebook X LinkedIn More