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PreprintCC BY 4.0arXiv

Equivariant multiplicities and torsion at attractive fixed points

  • Tao Gui
  • Peter L. Guo
  • Zhuowei Lin
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Abstract

Let X be a rationally smooth complex affine variety with a torus action and an attractive fixed point x. Suppose that X∖{x} is p-smooth and that its integral equivariant cohomology has no p-torsion. We prove that the order of its total p-primary cohomology torsion is the p-part of the reduced numerator of the equivariant multiplicity at x. In particular, this resolves the torsion-order conjecture of Juteau--Williamson and its local version for normal slices in Schubert varieties, using the equivariant torsion-freeness result of Fiebig--Williamson.

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Cite

BibTeXRIS
BibTeX
@misc{gui2026equivariant,
  title = {{Equivariant multiplicities and torsion at attractive fixed points}},
  author = {Tao Gui and Peter L. Guo and Zhuowei Lin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35600},
  eprint = {2609.35600},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35600},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Equivariant multiplicities and torsion at attractive fixed points
AU  - Tao Gui
AU  - Peter L. Guo
AU  - Zhuowei Lin
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.35600
UR  - https://arxiv.org/abs/2609.35600
AB  - Let X be a rationally smooth complex affine variety with a torus action and an attractive fixed point x. Suppose that X∖{x} is p-smooth and that its integral equivariant cohomology has no p-torsion. We prove that the order of its total p-primary cohomology torsion is the p-part of the reduced numerator of the equivariant multiplicity at x. In particular, this resolves the torsion-order conjecture of Juteau--Williamson and its local version for normal slices in Schubert varieties, using the equivariant torsion-freeness result of Fiebig--Williamson.
ER  -