16 citations · 72 across the 55 of their papers we have counts for
62 papers
Large imperfect fields are existentially closed in function fields after finite constant extension
Hagen Knaf, Franz-Viktor Kuhlmann
For an algebraic function field over a large field , we show: 1) if has a rational place, then there is a finite purely inseparable extension such that is…
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 which admits purely inseparable extensions o…
On certain definable coarsenings of valuation rings and their applications
Franz-Viktor Kuhlmann
We show how suitable extensions of prime degree of valued fields give rise to definable coarsenings of the valuation rings of and . In the case of Artin-Schreier a…
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…
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…
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 for equations and inequalities where and are final segments of ord…