F. Kuhlmann

collaborators

8 papers

math.AC2026

Topics in higher ramification theory I: ramification ideals

Franz-Viktor Kuhlmann

We introduce and study the notion of ramification ideals in higher ramification theory. After general results on their computation for finite extensions, we discuss their connectio…

math.AC2026

On algebraically maximal valued fields that are not defectless

Franz-Viktor Kuhlmann

An example originally given by F.~Delon shows the existence of an algebraically maximal discretely valued field of characteristic $p > 0$ which admits purely inseparable extensions o…

math.AC2026

Large imperfect fields are existentially closed in function fields after finite constant extension

Hagen Knaf, Franz-Viktor Kuhlmann

For an algebraic function field $F$ over a large field $K$ , we show: 1) if $F ∣ K$ has a rational place, then there is a finite purely inseparable extension $K^{'} ∣ K$ such that $K^{'}$ is…

math.LO2025

On certain definable coarsenings of valuation rings and their applications

Franz-Viktor Kuhlmann

We show how suitable extensions $(L ∣ K, v)$ of prime degree of valued fields give rise to definable coarsenings of the valuation rings of $L$ and $K$ . In the case of Artin-Schreier a…

math.LO2025

Model theory of tame valued fields and beyond: recent developments and open questions

Franz-Viktor Kuhlmann

We give a survey on recent developments in the model theory of valued fields since the introduction of the notion of ``tame valued field'', and of the modifications and generalizat…

math.AC2025

Arithmetic of cuts in ordered abelian groups and of ideals over valuation rings

Franz-Viktor Kuhlmann, Katarzyna Kuhlmann

We investigate existence, uniqueness and maximality of solutions $T$ for equations $S_{1} + T = S_{2}$ and inequalities $S_{1} + T \subseteq S_{2}$ where $S_{1}$ and $S_{2}$ are final segments of ord…