Structure des connexions méromorphes formelles de plusieurs variables et semi-continuité de l'irrégularité

Abstract

We prove Malgrange's conjecture on the absence of confluence phenomena for integrable meromorphic connections. More precisely, if $Y\to X$ is a complex-analytic fibration by smooth curves, $Z$ a hypersurface of $Y$ finite over $X$, and $\nabla$ an integrable meromorphic connection on $Y$ with poles along $Z$, then the function which attaches to {\smit x} $\in X$ the sum of the irregularities of the fiber ${\nabla }_{(x)}$ at the points of $Z_x$ is lower semicontinuous. The proof relies upon a study of the formal structure of integrable meromorphic connections in several variables.

44 pages. Submitted

References in corpus (3)

• Filtrations de type Hasse-Arf et monodromie p-adique
• De seriebus divergentibus
• An algebraic proof of Deligne's regularity criterion

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• Good formal structure for meromorphic flat connections on smooth projective surfaces
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• Swan conductors for p-adic differential modules, II: Global variation
• Characteristic cycle and wild ramification for nearby cycles of étale sheaves
• Relative singular support and the semi-continuity of characteristic cycles for étale sheaves
• An algebraic proof of Deligne's regularity criterion for integrable connections
• The Stokes phenomenon for an irregular Gelfand-Kapranov-Zelevinsky system associated with the rank one lattice
• Semi-continuity of conductors, and ramification bound of nearby cycles
• Logarithmic ramifications of étale sheaves by restricting to curves
• Cohomological boundedness for flat bundles on surfaces and applications