WHEN ARE THERE ENOUGH PROJECTIVE PERVERSE SHEAVES?

CIPRIANI, ALESSIO and WOOLF, JON (2022) WHEN ARE THERE ENOUGH PROJECTIVE PERVERSE SHEAVES? Glasgow Mathematical Journal, 64 (1). pp. 185-196.

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Official URL: http://dx.doi.org/10.1017/s0017089521000021

Abstract

<jats:title>Abstract</jats:title><jats:p>Let<jats:italic>X</jats:italic>be a topologically stratified space,<jats:italic>p</jats:italic>be any perversity on<jats:italic>X</jats:italic>and<jats:italic>k</jats:italic>be a field. We show that the category of<jats:italic>p</jats:italic>-perverse sheaves on<jats:italic>X</jats:italic>, constructible with respect to the stratification and with coefficients in<jats:italic>k</jats:italic>, is equivalent to the category of finite-dimensional modules over a finite-dimensional algebra if and only if<jats:italic>X</jats:italic>has finitely many strata and the same holds for the category of local systems on each of these. The main component in the proof is a construction of projective covers for simple perverse sheaves.</jats:p>

Item Type:	Article
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	25 Oct 2021 08:12
Last Modified:	30 Oct 2023 20:38
DOI:	10.1017/s0017089521000021
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3098927