Totally decomposable algebras with involution and R-triviality

arXiv (Cornell University) 2026 Preprint Open access

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Authors: M. Archita, Karim Johannès Becher
DOI: 10.48550/arxiv.2602.10302
Cited by: 0

Abstract

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 different from 2 is R-trivial. We further give an example showing that the statement does not extend to index 4 in the orthogonal case.

Fields of Study & Subjects

Advanced Algebra and Geometry Rings Modules and Algebras Algebraic Geometry and Number Theory

Publication details

Journal / source
arXiv (Cornell University)
Publication date
10 February 2026
Language
EN
Document type
Preprint