Abstract
In analogy with the classical theory of ordinary differential equations (see e.g. [6], [1], [5]), we define in this paper the notion regular singularity of a Drinfeld module at infinity. It turns out (Theorem (2.2)) that a Drinfeld module with regular singularity can not have a complex multiplication if the infinite place is of degree one, and has a tamely ramified period lattice which is of diamond shape. In §3, we study regular sigularity of φ-modules, which have more similar formalism to D -modules. We express the regularity of the singularity of φ-modules over a local field in four ways (Theorems (3.8) and (3.9)); (1) naively in terms of the valuations of the coefficients of certain polynomials, (2) by the existence of φ-stable lattices, (3) by the tameness of Galois actions, and (4) in terms of the norm of connections. For a field K , we denote by K a fixed separable closure of K , and let GK := Gal(K/K), the absolute Galois group of K .
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