https://u-paris.hal.science/hal-01697776v4Teyssier, Jean-BaptisteJean-BaptisteTeyssierIMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris CitéModuli of Stokes torsors and singularities of differential equationsHAL CCSD2022[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Teyssier, Jean-Baptiste2022-04-26 17:55:322023-03-24 14:53:262022-05-02 14:33:27enJournal articleshttps://u-paris.hal.science/hal-01697776v4/documenthttps://u-paris.hal.science/hal-01697776v3application/pdf4Let M be a meromorphic connection with poles along a smooth divisor D in a smooth algebraic variety. Let Sol M be the solution complex of M. We prove that the good formal decomposition locus of M coincides with the locus where the restrictions to D of Sol M and Sol End M are local systems. By contrast to the very different natures of these loci (the first one is defined via algebra, the second one is defined via analysis), the proof of their coincidence is geometric. It relies on the moduli of Stokes torsors.