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WHEN ARE THERE ENOUGH PROJECTIVE PERVERSE SHEAVES?

Part of: Homology and cohomology theories

Published online by Cambridge University Press:  15 March 2021

ALESSIO CIPRIANI  and
JON WOOLF
ALESSIO CIPRIANI
Affiliation:
Department of Mathematical Sciences, University of Liverpool, LiverpoolL69 7ZL, UK, e-mails: Alessio.Cipriani@liverpool.ac.uk, jonwoolf@liverpool.ac.uk
JON WOOLF
Affiliation:
Department of Mathematical Sciences, University of Liverpool, LiverpoolL69 7ZL, UK, e-mails: Alessio.Cipriani@liverpool.ac.uk, jonwoolf@liverpool.ac.uk
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Abstract

Let X be a topologically stratified space, p be any perversity on X and k be a field. We show that the category of p-perverse sheaves on X, constructible with respect to the stratification and with coefficients in k, is equivalent to the category of finite-dimensional modules over a finite-dimensional algebra if and only if X 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.

MSC classification

Secondary: 55N33: Intersection homology and cohomology
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 64 , Issue 1 , January 2022 , pp. 185 - 196
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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