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arXiv · 2602.22147

Similitudes over fields with I^4=0

M. Archita·Karim Johannes Becher
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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.

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M. Archita, Karim Johannes Becher. 2026-02-25. Similitudes over fields with I^4=0. https://arxiv.org/abs/2602.22147

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