Toroidalization of generating sequences in dimension two function fields of positive characteristic

TL;DR

This paper provides a characteristic-free proof that generating sequences of valuations in two-dimensional function fields can be toroidally structured under certain conditions, extending previous results to positive characteristic.

Contribution

It offers a characteristic-free proof of toroidalization of generating sequences in dimension two function fields, generalizing prior work to positive characteristic.

Findings

Established toroidal structure of generating sequences in positive characteristic

Extended Strong Monomialization results to a broader setting

Provided a characteristic-free proof approach

Abstract

We give a characteristic free proof of the main result of our previous paper (math.AC/0509697) concerning toroidalization of generating sequences of valuations in dimension two function fields. We show that when an extension of two dimensional algebraic regular local rings $R\subset S$ satisfies the conclusions of the Strong Monomialization theorem of Cutkosky and Piltant, the map between generating sequences in $R$ and $S$ has a toroidal structure.