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Using twisted nearby cycles, we define a new notion of slopes for complex holonomic
-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
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
. This generalizes the regularity of the Gauss–Manin connection proved by Griffiths, Katz and Deligne.
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