Schmid’s Formula for Higher Local Fields

Abstract

In local class field theory, the Schmid–Witt symbol encodes interesting data about the ramification theory of p-extensi-ons of K and can, for example, be used to compute the higher ramification groups of such extensions. In 1936, Schmid discovered an explicit formula for the Schmid–Witt symbol of Artin–Schreier extensions of local fields. Later, his formula was generalized to Artin–Schreier–Witt extensions, but still over a local field. In this paper we generalize Schmid’s formula to compute the Artin–Schreier–Witt– Parshin symbol for Artin–Schreier–Witt extensions of two-dimensional local fields of positive characteristic.