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arXiv · 2506.21717

Rational connectedness for groups of proper projective similitudes

M. Archita·Karim Johannes Becher
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Abstract

For a quadratic form $\varphi$ over a field of characteristic different from $2$, we study whether its group of proper projective similitudes ${\bf PSim}^+(\varphi)$ is rationally connected (i.e. $R$-trivial). We obtain new sufficient conditions in terms of structure properties of $\varphi$. We further provide new examples of quadratic forms $\varphi$ belonging to a given power of the fundamental ideal in the Witt ring and such that ${\bf PSim}^+(\varphi)$ is not rationally connected.

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M. Archita, Karim Johannes Becher. 2025-06-26. Rational connectedness for groups of proper projective similitudes. https://arxiv.org/abs/2506.21717

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