1 results
A boundedness theorem for nearby slopes of holonomic
${\mathcal{D}}$ -modules
- Part of
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- Journal:
- Compositio Mathematica / Volume 152 / Issue 10 / October 2016
- Published online by Cambridge University Press:
- 09 September 2016, pp. 2050-2070
- Print publication:
- October 2016
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- Article
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- You have access
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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.
