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math.NT2025
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…
math.NT2023
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_…
math.NT2017★ 8 cited
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…