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