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A boundedness theorem for nearby slopes of holonomic ${\mathcal{D}}$-modules

Part of: (Co)homology theory

Published online by Cambridge University Press:  09 September 2016

Jean-Baptiste Teyssier
Jean-Baptiste Teyssier*
Affiliation:
Hebrew University of Jerusalem, Einstein Institute for Mathematics, Givat Ram, Jerusalem, Israel email [email protected]
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Abstract

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Using twisted nearby cycles, we define a new notion of slopes for complex holonomic ${\mathcal{D}}$-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 ${\mathcal{E}}_{t}$ 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 ${\mathcal{E}}_{t}$. This generalizes the regularity of the Gauss–Manin connection proved by Griffiths, Katz and Deligne.

Keywords

D-modulenearby cyclesrapid decay homologyirregular periods

MSC classification

Primary: 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 10 , October 2016 , pp. 2050 - 2070
Copyright
© The Author 2016 

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