Good Formal Structures for Flat Meromorphic Connections, III: Irregularity and Turning Loci

Given a formal at meromorphic connection over an excellent scheme field of characteristic zero, in previous paper we established existence good structures and Deligne–Malgrange lattice after suitably blowing up. In this paper, reinterpret re fine these results by introducing some related structures. We consider the turning locus , which is set points one cannot achieve structure without show that when polar divisor has normal crossings, pure codimension 1 within divisor, hence 2 full space; had been previously André case smooth divisor. also construct irregularity sheaf its associated b-divisor, measure along divisors on blowups original generalizes another result semicontinuity curve fibration. One concrete consequence finements process for resolution functorial with respect to regular morphisms schemes; allows us transfer from schemes schemes, complex analytic varieties, nonarchimedean varieties.