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math.NT2025
Rational connectedness for groups of proper projective similitudes
M. Archita, Karim Johannes Becher
For a quadratic form over a field of characteristic different from , we study whether its group of proper projective similitudes is rationally connected (i…
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.NT2025
Bounds on the hermitian u-invariants under quadratic field extensions
Karim Johannes Becher, Fatma Kader Bingöl
The hermitian u-invariants of a central simple algebra with involution are studied. In this context, a new technique is obtained to give bounds for the behavior of these invariants…