Year: 2026
Type: preprint
Abstract: 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 fields of characteristic different from 2 over which every 9-dimensional quadratic form has a nontrivial zero. This includes function fields of p-adic curves and extensions of transcendence degree 3 of C. Main results of [28] and [29] are extended by relaxing the condition on the base field as well as on the Clifford invariant for orthogonal involutions.
Source: arXiv (Cornell University)
Authors: Archita, M., Becher, Karim Johannes
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7131663177
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