6 papers
The u-invariant of function fields in one variable
Karim Johannes Becher, Nicolas Daans, Vlerë Mehmeti
The u-invariant of a field is the largest dimension of an anisotropic quadratic torsion form over the field. In this article we obtain a bound on the u-invariant of function fields…
Variation of the Hausdorff dimension and degenerations of Schottky groups
Nguyen-Bac Dang, Vlerë Mehmeti
We show that the Hausdorff dimension of the limit set of a Schottky group varies continuously over the moduli space of Schottky groups defined over any complete valued field constr…
A survey of local-global methods for Hilbert's Tenth Problem
Sylvy Anscombe, Valentijn Karemaker, Zeynep Kisakürek +3
Hilbert's Tenth Problem (H10) for a ring R asks for an algorithm to decide correctly, for each , whether the diophantine equation $f(X_{1},...,X_…
An analytic viewpoint on the Hasse principle
Vlerë Mehmeti
Working on Berkovich analytic curves, we propose a geometric approach to the study of the Hasse principle over function fields of curves defined over a complete discretely valued f…
Patching over Analytic Fibers and the Local-Global Principle
Vlerë Mehmeti
As a starting point for higher-dimensional patching in the Berkovich setting, we show that this technique is applicable around certain fibers of a relative Berkovich analytic curve…
Patching over Berkovich Curves and Quadratic Forms
Vlerë Mehmeti
We extend field patching to the setting of Berkovich analytic geometry and use it to prove a local-global principle over function fields of analytic curves. We apply this result to…