English

Constructible sheaves are holonomic

Algebraic Geometry 2017-01-31 v8

Abstract

We show that for any constructible sheaf F on a smooth algebraic variety X over a field of arbitrary characteristic its singular support SS(F) is equidimensional of dimension dim X. Here SS(F) is the minimal closed subset of the cotangent bundle of X such that every (local) function on X with df(X) disjoint from SS(F) is locally acyclic relative to F.

Keywords

Cite

@article{arxiv.1505.06768,
  title  = {Constructible sheaves are holonomic},
  author = {Alexander Beilinson},
  journal= {arXiv preprint arXiv:1505.06768},
  year   = {2017}
}

Comments

21 pages. The previous version of the article was published in Selecta Mathematica 22 (2016), 1797--1819; in the present version the proof of a Kashiwara-Schapira theorem given in footnote 2 is simplified

R2 v1 2026-06-22T09:41:06.698Z