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arXiv · 2007.03060

Perverse sheaves and finite-dimensional algebras

Alessio Cipriani·Jon Woolf
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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.

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Alessio Cipriani, Jon Woolf. 2020-07-06. Perverse sheaves and finite-dimensional algebras. https://arxiv.org/abs/2007.03060

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