Kashiwara's Lemma for Potent D-modules

Abstract

On stacks there is a richer version of 𝒟-modules---called potent 𝒟−modules---which decompletes at equivariant parameters, in the same sense that genuine equivariant K-theory decompletes equivariant cohomology. In this paper, we prove a ``genuine'' version of Kashiwara's lemma for 𝒟-modules. Namely, we show that for a broad class of geometric stacks X, if Z ⊂ X is a closed substack, the category 𝒟^pot(Z) of potent 𝒟-modules on Z is equivalent under pushforward to the category 𝒟^pot _Z(X) of potent 𝒟-modules on X with support contained in Z.

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BibTeX RIS

BibTeX

@misc{erlikhman2026kashiwaras,
  title = {{Kashiwara's Lemma for Potent D-modules}},
  author = {Jacob Erlikhman and Kendric Schefers},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32003},
  eprint = {2610.32003},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32003},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Kashiwara's Lemma for Potent D-modules
AU  - Jacob Erlikhman
AU  - Kendric Schefers
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.32003
UR  - https://arxiv.org/abs/2610.32003
AB  - On stacks there is a richer version of 𝒟-modules---called potent 𝒟−modules---which decompletes at equivariant parameters, in the same sense that genuine equivariant K-theory decompletes equivariant cohomology. In this paper, we prove a ``genuine'' version of Kashiwara's lemma for 𝒟-modules. Namely, we show that for a broad class of geometric stacks X, if Z ⊂ X is a closed substack, the category 𝒟^pot(Z) of potent 𝒟-modules on Z is equivalent under pushforward to the category 𝒟^pot _Z(X) of potent 𝒟-modules on X with support contained in Z.
ER  -

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