Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characteristic cycle of a rank one sheaf and ramification theory   We compute the characteristic cycle of a rank one sheaf on a smooth surface
over a perfect field of positive characteristic. We construct a canonical
lifting on the cotangent bundle of Kato's logarithmic characteristic cycle
using ramification theory and prove the equality of the characteristic cycle
and the canonical lifting. As corollaries, we obtain a computation of the
singular support in terms of ramification theory.

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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph