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Dualité et comparaison pour les complexes de de Rham logarithmiques par rapport aux diviseurs libres

Francisco Javier Calderón Moreno; Luis Narváez Macarro — 2005

Annales de l’institut Fourier

Soit $X$ une variété analytique complexe lisse et $D \subset X$ un diviseur libre. Les connexions logarithmiques intégrables par rapport à $D$ peuvent être étudiées comme des $𝒪_{X}$ -modules localement libres munis d’une structure de module (à gauche) sur l’anneau $𝒟_{X} (log D)$ des opérateurs différentiels logarithmiques . Dans cet article nous étudions deux résultats liés : la relation entre les duaux d’une connexion logarithmique intégrable sur les anneaux de base $𝒟_{X}$ et $𝒟_{X} (log D)$ , et un critère différentiel pour le théorème de comparaison...

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