Rational connectedness for groups of proper projective similitudes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912452967399424 |
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| author | Archita, M. Becher, Karim Johannes |
| author_facet | Archita, M. Becher, Karim Johannes |
| contents | For a quadratic form $φ$ over a field of characteristic different from $2$, we study whether its group of proper projective similitudes ${\bf PSim}^+(φ)$ is rationally connected (i.e. $R$-trivial).
We obtain new sufficient conditions in terms of structure properties of $φ$. We further provide new examples of quadratic forms $φ$ belonging to a given power of the fundamental ideal in the Witt ring and such that ${\bf PSim}^+(φ)$ is not rationally connected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rational connectedness for groups of proper projective similitudes Archita, M. Becher, Karim Johannes Number Theory Algebraic Geometry Rings and Algebras 11E04, 11E57, 11E81, 14E08, 20G15 For a quadratic form $φ$ over a field of characteristic different from $2$, we study whether its group of proper projective similitudes ${\bf PSim}^+(φ)$ is rationally connected (i.e. $R$-trivial). We obtain new sufficient conditions in terms of structure properties of $φ$. We further provide new examples of quadratic forms $φ$ belonging to a given power of the fundamental ideal in the Witt ring and such that ${\bf PSim}^+(φ)$ is not rationally connected. |
| title | Rational connectedness for groups of proper projective similitudes |
| topic | Number Theory Algebraic Geometry Rings and Algebras 11E04, 11E57, 11E81, 14E08, 20G15 |
| url | https://arxiv.org/abs/2506.21717 |