English

Holonomic \'etale sheaves are constructible

Algebraic Geometry 2024-10-08 v1

Abstract

Building on Beilinson's work, ``constructible sheaves are holonomic,'' we introduce the notion of holonomicity for \'etale sheaves, without assuming a priori constructibility. Over a perfect base field, we establish the converse of Beilinson's result, showing that holonomic sheaves are indeed constructible. This can be seen as an \'etale analogue of Kashiwara's theorem on holonomic DX{\mathcal D}_X-modules.

Keywords

Cite

@article{arxiv.2410.04677,
  title  = {Holonomic \'etale sheaves are constructible},
  author = {Ahmed Abbes and Takeshi Saito},
  journal= {arXiv preprint arXiv:2410.04677},
  year   = {2024}
}

Comments

12 pages

R2 v1 2026-06-28T19:10:36.789Z