The local information of difference equations
The local information of difference equations
复制标题
差分方程的局部信息
DOI：
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发表时间：
2018
期刊：
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通讯作者：
Mois'es Herrad'on Cueto
中科院分区：
文献类型：
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作者：
Mois'es Herrad'on Cueto
我们给出了仿射线上差分模对轨道正式邻域的限制的定义，试图模仿 D 模的类似定义和属性。我们通过两种方式证明这个定义是合理的。首先，我们证明在仿射线上指定差分模相当于给出其对轨道补集的限制，以及对轨道邻域的限制以及两者对交集的限制之间的同构。我们还给出了差分模块的消失循环的定义，并定义了局部梅林变换，它是差分模块的消失循环与其梅林变换（D 模块）的附近循环之间的等价。
We give a definition for the restriction of a difference module on the affine line to a formal neighborhood of an orbit, trying to mimic the analogous definition and properties for a D-module. We show that this definition is reasonable in two ways. First, we show that specifying a difference module on the affine line is equivalent to giving its restriction to the complement of an orbit, together with its restriction to a neighborhood of an orbit and an isomorphism between the restriction of both to the intersection. We also give a definition for vanishing cycles of a difference module and define a local Mellin transform, which is an equivalence between vanishing cycles of a difference module and nearby cycles of its Mellin transform, a D-module.