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Isotropy of symplectic involutions and motivic equivalence for groups of type sfC

  • 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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Cite

BibTeXRIS
BibTeX
@misc{barry2026isotropy,
  title = {{Isotropy of symplectic involutions and motivic equivalence for groups of type $\sfC$}},
  author = {Demba Barry and Charles De Clercq and Anne Quéguiner-Mathieu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25363},
  eprint = {2610.25363},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25363},
}
RIS
TY  - UNPB
TI  - Isotropy of symplectic involutions and motivic equivalence for groups of type sfC
AU  - Demba Barry
AU  - Charles De Clercq
AU  - Anne Quéguiner-Mathieu
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25363
UR  - https://arxiv.org/abs/2610.25363
AB  - 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.
ER  -