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.
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