Corrections and Notes for the Paper "Value groups, residue fields and bad places of rational function field" [arXiv:1003.5685]

TL;DR

This paper corrects errors in a previous mathematical work on valuation theory and reports new developments that resolve previously open cases, advancing understanding in the field.

Contribution

It provides corrections to an earlier influential paper and introduces recent results that settle open problems in valuation theory of rational function fields.

Findings

Corrections to the original paper’s mistakes

Resolution of open cases in valuation theory

New developments advancing the field

Abstract

We correct mistakes in the paper Kuhlmann, F.-V.: Value groups, residue fields and bad places of rational function fields, Trans. Amer. Math. Soc. 356 (2004) [arXiv:1003.5685] and report on recent new developments which settle cases left open in that paper.