Schmid's Formula for Higher Local Fields
Number Theory
2021-04-27 v2
Abstract
In local class field theory, the Schmid-Witt symbol encodes interesting data about the ramification theory of -extensi-ons of 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.
Cite
@article{arxiv.1709.04559,
title = {Schmid's Formula for Higher Local Fields},
author = {Matthew Schmidt},
journal= {arXiv preprint arXiv:1709.04559},
year = {2021}
}