25 citations · 95 across the 28 of their papers we have counts for
12 papers · 1 filter
A radical answer to a question by Robinson
Blaise Boissonneau, Mikel E. Garciarena, Immanuel Halupczok
We study the ring of Puiseux polynomials with integer coefficients. We prove notably that the order given by the leading coefficient is definable without parameters in the language…
On simple groups definable in some valued fields
Jakub Gismatullin, Immanuel Halupczok, Dugald Macpherson
We prove that non-abelian definable, definably simple groups in 1-h-minimal henselian valued fields are essentially already linear algebraic groups. Here, the group is assumed to l…
Spherically complete models of Hensel minimal valued fields
David Bradley-Williams, Immanuel Halupczok
We prove that Hensel minimal expansions of finitely ramified Henselian valued fields admit spherically complete immediate elementary extensions. More precisely, the version of Hens…
Hensel minimality II: Mixed characteristic and a diophantine application
Raf Cluckers, Immanuel Halupczok, Silvain Rideau-Kikuchi +1
In this paper together with the preceding Part I \cite{CHR}, we develop a framework for tame geometry on Henselian valued fields of characteristic zero, called Hensel minimality. I…
Definable sets up to definable bijections in Presburger groups
Raf Cluckers, Immanuel Halupczok
We entirely classify definable sets up to definable bijections in -groups, where the language is the one of ordered abelian groups. From this, we deduce, among others,…
Integration of functions of motivic exponential class, uniform in all non-archimedean local fields of characteristic zero
Raf Cluckers, Immanuel Halupczok
Through a cascade of generalizations, we develop a theory of motivic integration which works uniformly in all non-archimedean local fields of characteristic zero, overcoming some o…