D-MODULES ON INFINITE DIMENSIONAL VARIETIES
D-MODULES ON INFINITE DIMENSIONAL VARIETIES
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无限维变量的 D 模块
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
S. Raskin
中科院分区：
文献类型：
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作者：
S. Raskin
1.2.我们与之抗争的基本特征是，有两种类型的无限维度在起作用：前无限维度和无无限维度。也就是说，我们可以有一个无限维簇S，它是有限维簇的并S“一思”，或者T，它是有限维簇的射影极限T“limj Tj”，例如无限型格式。任何合理的D-模理论都会产生一些De-Rham同调和上同调群。我们假设这些群应该取离散向量空间中的值作为基本原则，也就是说，我们希望避免投影极限。然后，在无限维的情况下，自然理论是S的同源：
1.2. The basic feature that we struggle against is that there are two types of infinite dimensionality at play: pro-infinite dimensionality and ind-infinite dimensionality. That is, we could have an infinite dimensional variety S that is the union S “ YiSi “ colimiSi of finite dimensional varieties, or T that is the projective limit T “ limj Tj of finite dimensional varieties, e.g., a scheme of infinite type. Any reasonable theory of D-modules will produce produce some kinds of de Rham homology and cohomology groups. We postulate as a basic principle that these groups should take values in discrete vector spaces, that is, we wish to avoid projective limits. Then, in the ind-infinite dimensional case, the natural theory is the homology of S: