Perverse sheaves and finite-dimensional algebras
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2020
- DOI:
- 10.48550/arXiv.2007.03060
- arXiv:
- arXiv:2007.03060
- Bibcode:
- 2020arXiv200703060C
- Keywords:
-
- Mathematics - Representation Theory;
- Mathematics - Algebraic Topology;
- 18G80 (Primary);
- 55N33 (Secondary)
- E-Print:
- 11 pages