Extensions of truncated discrete valuation rings II

TL;DR

This paper establishes an equivalence between categories of ramified extensions of a complete discrete valuation field and its truncated valuation ring, providing a new perspective on their structural relationship.

Contribution

It introduces a categorical equivalence linking ramified extensions of a valuation field with those of its truncated ring, extending previous results to a broader context.

Findings

Categorical equivalence between ramified extensions and truncated rings

Extension of previous work to higher ramification levels

Provides a new framework for understanding ramification in valuation theory

Abstract

An equivalence is established between the category of at most $a$-ramified finite separable extensions of a complete discrete valuation field $K$ and the category of at most $a$-ramified finite extensions of the "length-$a$ truncation" $\OK/\mK^a$ of the integer ring of $K$.