Structure the flat meromorphic connections of several variables and semi-continuity of the irregularity

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 del an integrable meromorphic connection on Y with poles along Z, then the function which attaches to x is an element of X the sum of the irregularities of the fiber del((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.