Achinger: Regular logarithmic connections

We extend Deligne's results on regular connections (LNM 163) to log schemes over C. More precisely, we develop a notion of regularity (at infinity) for integrable connections on idealized log smooth log schemes, and prove that the analytification functor induces an equivalence between the categories of regular algebraic connections and of integrable connections on the analytification. By the work of Ogus, the latter category can be described in terms of certain constructible sheaves on the Kato-Nakayama space. This is part of a project in progress whose goal is to obtain a Riemann-Hilbert correspondence for smooth rigid-analytic spaces over C((t)).