9 papers
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…
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…
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…
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…
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…
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…