Higher criteria for the regularity of a one-dimensional local field

Abstract

The concept of irregularity of formal modules in one-dimensional local fields is considered. A connection is obtained between the irregularity of all unramified extensions M/L and the ramification index eL/K for a sufficiently wide class of formal groups. The notion of s-irregularity for natural s is introduced (generalization of the notion of irregularity to the case of roots [πs]), and similar criteria for irregularity are proved for it for the case of generalized and relative formal Lubin—Tate modules.