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

By Y. Andr'e. 2007

48 citations recorded by the source corpus.

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

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/cfc5ab56a53934b5eec6c90b7a824dd6a4b3ac2e

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In Applied Mathematics

1. C. Sabbah
2. Y. Andr'e

In Geometry and Topology

1. C. Sabbah
2. Y. Andr'e
3. Kiran S. Kedlaya
4. H. Iritani
5. Laurent Berger
6. Étienne Mann

Citations in the corpus

• Slope filtrations (2008, background): “is lower semicontinuous [7] (as was conjectured by Malgrang e).”
• Introduction to Stokes Structures (2009, background): “— For a sheaf F on S(1), its Poincaré-Verdier dual DF is RHomC(F ,kS1 [1]) and we denote by D ′ F = RHomC(F ,kS1) the shifted complex.”