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math.NT2026
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…
math.NT2026
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…
math.NT2026
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…