Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The local information of difference equations   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.

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The categories of this paper are: cs
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The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: physics
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg