Non-$R$-trivial proper projective similitudes in type $A_3\equiv D_3$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910205660364800 |
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| author | Archita, M. Becher, Karim Johannes |
| author_facet | Archita, M. Becher, Karim Johannes |
| contents | Over an arbitrary field of characteristic different from $2$ admitting an anisotropic torsion $3$-fold Pfister form, we apply a construction due to Merkurjev to produce an algebra with orthogonal involution of degree $6$ which admits proper projective similitudes that are not $R$-trivial. In particular, such examples exist over every finitely generated transcendental extension of a local or global number field, as well as over every finitely generated extension of transcendence degree $3$ of $\mathbb{R}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09110 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-$R$-trivial proper projective similitudes in type $A_3\equiv D_3$ Archita, M. Becher, Karim Johannes Number Theory Algebraic Geometry K-Theory and Homology Rings and Algebras Over an arbitrary field of characteristic different from $2$ admitting an anisotropic torsion $3$-fold Pfister form, we apply a construction due to Merkurjev to produce an algebra with orthogonal involution of degree $6$ which admits proper projective similitudes that are not $R$-trivial. In particular, such examples exist over every finitely generated transcendental extension of a local or global number field, as well as over every finitely generated extension of transcendence degree $3$ of $\mathbb{R}$. |
| title | Non-$R$-trivial proper projective similitudes in type $A_3\equiv D_3$ |
| topic | Number Theory Algebraic Geometry K-Theory and Homology Rings and Algebras |
| url | https://arxiv.org/abs/2605.09110 |