9 papers
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…
Totally decomposable algebras with involution and R-triviality
M. Archita, Karim Johannes Becher
We show that the group of proper projective similitudes of a totally decomposable algebra with orthogonal or symplectic involution of index at most 2 over a field of characteristic…
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…