论文标题
$ a \ Mathcal {V} $ - 模块和微分操作员的歼灭器
Annihilators of $A\mathcal{V}$-modules and differential operators
论文作者
论文摘要
对于平滑的代数品种$ x $，我们研究了$ x $的功能环有限生成的模块类别，该模块具有lie algebra $ \ mathcal \ mathcal {v} $的$ x $上的多项式矢量字段的兼容动作。我们表明，$ \ Mathcal {V} $的关联表示，取决于订单的差分运算符，具体取决于模块的等级。差分运算符的顺序提供了对表示复杂性的自然度量，最简单的情况是$ d $模型的情况。
For a smooth algebraic variety $X$, we study the category of finitely generated modules over the ring of function of $X$ that has a compatible action of the Lie algebra $\mathcal{V}$ of polynomials vector fields on $X$. We show that the associated representation of $\mathcal{V}$ is given by a differential operator of order depending on the rank of the module. The order of the differential operator provides a natural measure of the complexity of the representation, with the simplest case being that of $D$-modules.
