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 (1)

• An algebraic proof of Deligne's regularity criterion

Cited by in corpus (3)

• Good formal structure for meromorphic flat connections on smooth projective surfaces
• Swan conductors for p-adic differential modules, II: Global variation
• An algebraic proof of Deligne's regularity criterion for integrable connections