Rational connectedness for groups of proper projective similitudes

2025/06/26 by Archita, M., Becher, Karim Johannes
#11E04 #11E57 #11E81 #14E08 #20G15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2506.21717

Abstract

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.

Citations

• The u-invariant of function fields in one variable
• More Examples of Non-Rational Adjoint Groups
• Hyperbolicity of orthogonal involutions

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