Perverse \(t\)-structure on Artin stacks
type: Item
instance of: scholarly article
title: Perverse \(t\)-structure on Artin stacks
zbMATH Open document ID: 1188.14002
author: Yves Laszlo
author: Martin Olsson
published in: Mathematische Zeitschrift
publication date: 2009-03-26T00:00:00Z
review text: The article under review gives an account of the basic theory of perverse sheaves, with finite or adic coefficients, on an Artin stack \(\mathcal X\) locally of finite type over a field \(k\). Its main contribution is to define the category of perverse sheaves on \(\mathcal X\) in a way that mimics the usual definition for schemes, namely as the heart of a \(t\)-structure on an appropriate derived category of constructible sheaves on \(\mathcal X\); and to show that this is essentially the only possible definition compatible with the usual definition of perverse sheaves on a scheme and with descent. The article also contains basic material on middle extensions; Artinianness and Noetherianness of the category of perverse sheaves with \(\mathbb Q_l\)-coefficients for \(l \in k^\times\), and a characterization of the simple perverse sheaves in this case; and the theory of weights when \(k\) is finite.
Mathematics Subject Classification ID: 14A20
Mathematics Subject Classification ID: 18E30
zbMATH DE Number: 5533149
zbMATH Keywords: Artin stack
zbMATH Keywords: perverse sheaf
reviewed by: Brian Smithling
MaRDI profile type: Publication
full work available at URL: s00209-008-0348-z
OpenAlex ID: W2046843384
cites work: Q2736012
cites work: The six operations for sheaves on Artin stacks. I: Finite coefficients
cites work: The six operations for sheaves on Artin stacks. II: Adic coefficients
cites work: Triangulated categories
DOI: 10.1007/S00209-008-0348-Z
description: scientific article; zbMATH DE number 5533149