\(\nabla\)-Poincaré's lemma and \(\nabla\)-de Rham cohomology for an integrable connection with irregular singular points (Q789574)

The author announces results on the exactness, under certain conditions, of the sequences \(S^-(^*H)\to^{\nabla}S^-\Omega^ 1(^*H)\to^{\nabla}...\to^{\nabla}S^-\Omega^ n(^*H)\to^{\nabla}0\) and \(S^-\!_ 0\to^{\nabla}S^-\!_ 0\Omega^ 1\to^{\nabla}...\to^{\nabla}S^-\!_ 0\Omega^ n\to^{\nabla}0\) where \(\Omega^ p(^*H)=\) sheaf of germs of meromorphic p-forms on the complex manifold M, \(\dim_{{\mathbb{C}}}M=n,\) which are holomorphic in M-H, H a divisor on M. The notions used and the details of proof are explained elsewhere, cf. the author's preprint ''\(\nabla\)-Poincaré's lemma and an isomorphism theorem of De Rham type in asymptotic analysis''.