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Moduli of Stokes torsors and singularities of differential equations

Abstract : Let 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.
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https://hal-univ-paris.archives-ouvertes.fr/hal-01697776
Contributor : Jean-Baptiste Teyssier <>
Submitted on : Thursday, March 7, 2019 - 4:41:01 PM
Last modification on : Friday, October 2, 2020 - 3:28:26 AM
Long-term archiving on: : Sunday, June 9, 2019 - 10:06:37 AM

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  • HAL Id : hal-01697776, version 3
  • ARXIV : 1802.00289

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Jean-Baptiste Teyssier. Moduli of Stokes torsors and singularities of differential equations. 2019. ⟨hal-01697776v3⟩

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