9 papers · 1 filter
Fields where torsion forms decompose
M. Archita, Karim Johannes Becher
Over a real field which is an extension of transcendence degree 1 of a hereditarily pythagorean base field, every quadratic form which is torsion decomposes into an orthogonal sum…
Non--trivial proper projective similitudes in type
M. Archita, Karim Johannes Becher
Over an arbitrary field of characteristic different from admitting an anisotropic torsion -fold Pfister form, we apply a construction due to Merkurjev to produce an algebra…
Similitudes over fields with I^4=0
M. Archita, Karim Johannes Becher
This article studies the set of R-equivalence classes of the group of proper projective similitudes of an algebra with involution of the first kind. The main results concern base f…
Uniform existential definitions of valuations in function fields in one variable
Karim Johannes Becher, Nicolas Daans, Philip Dittmann
We study function fields of curves over a base field which is either a global field or a large field having a separable field extension of degree divisible by . We show that…
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…
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…