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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…
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…