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

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Let X be a complex analytic manifold and D ⊂ X a free divisor. Integrable logarithmic connections along D can be seen as locally free Oₓ-modules endowed with a (left) module structure over the ring of logarithmic differential operators Dₓ(D). In this paper we study two related results: the relationship between the duals of any integrable logarithmic connection over the base rings Dₓ and Dₓ(D), and a differential criterion for the logarithmic comparison theorem. We also generalize a formula of Esnault-Viehweg in the normal crossing case for the Verdier dual of a logarithmic de Rham complex.