English

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 vv-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 vv-function is determined by ramification filtration. In this paper, we give a formula for the vv-function for 2-dimensional representations of the bicyclic group of order p2p^2 with pp the characteristic of our base field. Using this formula, we construct an example of vv-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}
}