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.

中文翻译：

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什么时候有足够的投射性变态？

让X是一个拓扑分层的空间，p任性X和ķ成为一个领域。我们证明了类别p- 反常的滑轮X, 可构造关于分层和系数ķ, 等价于有限维代数上的有限维模的范畴当且仅当X具有有限多个层，并且对于每个层上的局部系统类别也是如此。证明中的主要组成部分是简单的反滑轮的投影覆盖结构。