1 citations · 1 across the 8 of their papers we have counts for
10 papers
AKE principles in roughly deeply ramified henselian valued fields
Franziska Jahnke, Margarete Ketelsen, Floris Vermeulen
We show that for any henselian valued field of mixed characteristic , the (existential) -theory of the valued field is determined by the (existen…
Ordered henselian valued fields: definability and Borel sets
Lothar Sebastian Krapp, Floris Vermeulen
We firstly show that due to their resplendency ordered henselian valued fields admit relative field quantifier elimination in the Denef--Pas language expanded by linear orders in t…
The Grothendieck ring of a non-divisible ordered abelian group is trivial
Blaise Boissonneau, Mathias Stout, Floris Vermeulen
We consider the model-theoretic Grothendieck ring of definable sets in ordered abelian groups. It is well-known that and $\mat…
Integration in Hensel minimal fields
Mathias Stout, Floris Vermeulen
We develop a framework of motivic integration in the style of Hrushovski--Kazhdan in arbitrary Hensel minimal fields of equicharacteristic zero. Hence our work generalizes that of…
Counting rational points on transcendental curves in valued fields
Floris Vermeulen
We prove upper bounds on the number of rational points on transcendental curves in arbitrary -h-minimal fields, similar to the Pila--Wilkie counting theorem in the o-minimal set…
Serre's question on thin sets in projective space
Tijs Buggenhout, Raf Cluckers, Per Salberger +2
We answer a question of Serre from the 1980s on rational points of bounded height on projective thin sets, in degree at least . For degrees and we improve the known boun…
A geometric determinant method and geometric dimension growth
Tijs Buggenhout, Yotam I. Hendel, Floris Vermeulen
We study a geometric version of the dimension growth conjecture. While it is closely related in spirit to themes arising in geometric Manin's conjecture, it applies in greater gene…
Motivic Mellin transforms
Raf Cluckers, François Loeser, Kien Huu Nguyen +1
This work brings Mellin transforms into the realm of motivic integration. The new, larger class of motivic functions is stable under motivic Mellin and Fourier transforms, with gen…
Almost real closed fields with real analytic structure
Kien Huu Nguyen, Mathias Stout, Floris Vermeulen
Cluckers and Lipshitz have shown that real closed fields equipped with real analytic structure are o-minimal. This generalizes the well-known subanalytic structure $\mathbb{R}_{\ma…
Improvements on dimension growth results and effective Hilbert's irreducibility theorem
Raf Cluckers, Pierre Dèbes, Yotam I. Hendel +2
We sharpen and generalize the dimension growth bounds for the number of points of bounded height lying on an irreducible algebraic variety of degree , over any global field. In…