4 citations · 9 across the 10 of their papers we have counts for
11 papers
Dimension growth for affine varieties
Floris Vermeulen
We prove uniform upper bounds on the number of integral points of bounded height on affine varieties. If is an irreducible affine variety of degree in …
Scrollar invariants, syzygies and representations of the symmetric group II
Floris Vermeulen
Let be a degree cover of curves. In work by Castryck, Zhao and the author, we showed how one can attach to each partition of a multi-set of scrol…
Arithmetically equivalent number fields have approximately the same successive minima
Floris Vermeulen
Let and be arithmetically equivalent number fields, both of degree . We prove that and have the same successive minima, up to a constant depending only on .…
Hensel minimality: Geometric criteria for -h-minimality
Floris Vermeulen
Recently, Cluckers, Halupczok and Rideau-Kikuchi developed a new axiomatic framework for tame non-Archimedean geometry, called Hensel minimality. It was extended to mixed character…
On abelian covers of the projective line with fixed gonality and many rational points
Xander Faber, Floris Vermeulen
A smooth geometrically connected curve over the finite field with gonality has at most rational points. The first author and Grantham conjectured that…
Scrollar invariants, syzygies and representations of the symmetric group
Wouter Castryck, Floris Vermeulen, Yongqiang Zhao
We give an explicit minimal graded free resolution, in terms of representations of the symmetric group , of a Galois-theoretic configuration of points in $\mathbb{P}^{d-2}…
A Pila--Wilkie theorem for Hensel minimal curves
Victoria Cantoral-Farfán, Kien Huu Nguyen, Mathias Stout +1
Recently, a new axiomatic framework for tameness in henselian valued fields was developed by Cluckers, Halupczok, Rideau-Kikuchi and Vermeulen and termed Hensel minimality. In this…
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…
Curves of fixed gonality with many rational points
Floris Vermeulen
Given an integer and an odd prime power we show that for every large genus there exists a non-singular curve defined over of genus and gona…
Points of bounded height on curves and the dimension growth conjecture over
Floris Vermeulen
In this article we prove several new uniform upper bounds on the number of points of bounded height on varieties over . For projective curves, we prove the analogu…
Lifting low-gonal curves for use in Tuitman's algorithm
Wouter Castryck, Floris Vermeulen
Consider a smooth projective curve over a finite field , equipped with a simply branched morphism of degree .…