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

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 Z _x is lower semicontinuous. The proof relies upon a study of the formal structure of integrable meromorphic connections in several variables.