English

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 pp-extensi-ons of KK 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}
}
R2 v1 2026-06-22T21:42:33.204Z