5 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…
R-triviality for adjoint classical groups of type C
M. Archita
For a central simple algebra with a symplectic involution (A,s) over a field of characteristic different from 2, we show that its group of projective similitudes PSim(A,s) is R-tri…
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…