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PreprintCC BY 4.0arXiv

On the normality of the commuting scheme

  • Jack Sempliner
  • Xiangqian Yang
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Abstract

If G is a connected reductive algebraic group over a field k of characteristic ℓ, we show that both the Lie-theoretic and group-theoretic commuting schemes associated to G are normal and Cohen--Macaulay when ℓ = 0, or ℓ is larger than the Coxeter numbers of all simple factors of G, and that ℓ ≠ 19 (resp. ℓ ≠ 31) when G has a simple factor of type E7 (resp. E8). The main new ingredients are provided by studying the unipotent categorical Langlands functor of Zhu. Along the way we prove a t-exactness result for a finite unipotent categorical Langlands functor which may be of independent interest.

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Cite

BibTeXRIS
BibTeX
@misc{sempliner2026normality,
  title = {{On the normality of the commuting scheme}},
  author = {Jack Sempliner and Xiangqian Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27360},
  eprint = {2609.27360},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27360},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the normality of the commuting scheme
AU  - Jack Sempliner
AU  - Xiangqian Yang
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.27360
UR  - https://arxiv.org/abs/2609.27360
AB  - If G is a connected reductive algebraic group over a field k of characteristic ℓ, we show that both the Lie-theoretic and group-theoretic commuting schemes associated to G are normal and Cohen--Macaulay when ℓ = 0, or ℓ is larger than the Coxeter numbers of all simple factors of G, and that ℓ ≠ 19 (resp. ℓ ≠ 31) when G has a simple factor of type E_7 (resp. E_8). The main new ingredients are provided by studying the unipotent categorical Langlands functor of Zhu. Along the way we prove a t-exactness result for a finite unipotent categorical Langlands functor which may be of independent interest.
ER  -