A boundedness theorem for nearby slopes of holonomic D-modules. (9th September 2016) - Teyssier, Jean-Baptiste
Abstract : Using twisted nearby cycles, we define a new notion of slopes for complex holonomic D -modules. We prove a boundedness result for these slopes, study their functoriality and use them to characterize regularity. For a family of (possibly irregular) algebraic connections E_t parametrized by a smooth curve, we deduce under natural conditions an explicit bound for the usual slopes of the differential equation satisfied by the family of irregular periods of the E_t . This generalizes the regularity of the Gauss–Manin connection proved by Griffiths, Katz and Deligne.