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arXiv · 2610.25363

Isotropy of symplectic involutions and motivic equivalence for groups of type $\sf{C}$

Demba Barry·Charles De Clercq·Anne Quéguiner-Mathieu
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Abstract

We extend to arbitrary characteristic a theorem due to Karpenko and Tignol on the isotropy of symplectic involutions after generic index reduction; as a consequence, we also prove the existence of critical varieties for semi-simple algebraic groups of type $\sf C$ over arbitrary base fields. The latter result relies on a characteristic-free argument, which involves the computation of the mod $2$ Tate trace of the variety of isotropic ideals of reduced dimension $2$ for a symplectic involution.

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Demba Barry, Charles De Clercq, Anne Quéguiner-Mathieu. 2026-10-18. Isotropy of symplectic involutions and motivic equivalence for groups of type $\sf{C}$. https://arxiv.org/abs/2610.25363

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