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PreprintCC BY 4.0arXiv

Torsion proliferation

  • Joseph Baine
  • Daniel Tubbenhauer
Open at sourcePDFDOICite

Abstract

This paper considers the generic behaviour of sheaves supported on Schubert varieties in finite flag varieties. Our main results are that, for any fixed prime p, as the rank of the associated algebraic group grows, almost every intersection cohomology sheaf admits p-torsion in its stalks or costalks, and almost every indecomposable parity sheaf is not perverse. For certain families of partial flag varieties we also determine explicit asymptotics for this growth.

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Cite

BibTeXRIS
BibTeX
@misc{baine2026torsion,
  title = {{Torsion proliferation}},
  author = {Joseph Baine and Daniel Tubbenhauer},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31781},
  eprint = {2609.31781},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31781},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Torsion proliferation
AU  - Joseph Baine
AU  - Daniel Tubbenhauer
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.31781
UR  - https://arxiv.org/abs/2609.31781
AB  - This paper considers the generic behaviour of sheaves supported on Schubert varieties in finite flag varieties. Our main results are that, for any fixed prime p, as the rank of the associated algebraic group grows, almost every intersection cohomology sheaf admits p-torsion in its stalks or costalks, and almost every indecomposable parity sheaf is not perverse. For certain families of partial flag varieties we also determine explicit asymptotics for this growth.
ER  -