On the representation type of local twisted group rings

Abstract

The purpose of this paper is to examine locally the representation type of twisted group rings. It is proved that a twisted group ring over a local field is of finite representation type if and only if | G 1| = 3 and G 1 ≠ G 2, or | G 1| ⩽ 2, where G 1 is the ith ramification group of the extension, i = 1, 2.