论文标题
不良的滑根和有限维代数
Perverse sheaves and finite-dimensional algebras
论文作者
论文摘要
让$ x $成为拓扑结构的空间，$ p $为$ x $上的任何变态，而$ k $是一个字段。我们表明，$ p $ p $ perverse Sheaves在$ x $上，相对于分层构建，并且具有$ k $的系数，相当于有限维模块的类别，而当$ x $具有一定的阶层，并且在每个类别的局部系统上都有有限维代数。证明中的主要组成部分是用于简单变形绳索的投影覆盖物的构造。
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.
