Multi angle Skeletons and moduli of Stokes torsors
Auteurs : Teyssier, Jean-Baptiste (Auteur de la Conférence)
CIRM (Editeur )
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Résumé : In the local classification of differential equations of one complex variable, torsors under a certain sheaf of algebraic groups (the Stokes sheaf) play a central role. On the other hand, Deligne defined in positive characteristic a notion of skeletons for l-adic local systems on a smooth variety, constructed an algebraic variety parametrizing skeletons and raised the question wether every skeleton comes from an actual l-adic local system. We will explain how to use a variant of Deligne's skeleton conjecture in characteristic 0 to prove the existence of an algebraic variety parametrizing Stokes torsors. We will show how the geometry of this moduli can be used to prove new finiteness results on differential equations.Codes MSC :
14F10 - Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
32C38 - Sheaves of differential operators and their modules, D-modules