The v-function in the wild McKay correspondence is not determined by the ramification filtration
Algebraic Geometry
2021-07-09 v1 Number Theory
Abstract
The -function appears in the wild McKay correspondence and it is an invariant of a Galois extension over a local field which measures about the ramification of extension. The ramification filtration is also such invariant. Yasuda presented the problem whether the -function is determined by ramification filtration. In this paper, we give a formula for the -function for 2-dimensional representations of the bicyclic group of order with the characteristic of our base field. Using this formula, we construct an example of -function not determined by the ramification filtration.
Keywords
Cite
@article{arxiv.2107.03511,
title = {The v-function in the wild McKay correspondence is not determined by the ramification filtration},
author = {Takahiro Yamamoto},
journal= {arXiv preprint arXiv:2107.03511},
year = {2021}
}