Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vologodsky integration on curves with semi-stable reduction   We prove that the Vologodsky integral of a mermorphic one-form on a curve
over a $p$-adic field with semi-stable reduction restrict to Coleman integrals
on the rigid subdomains reducing to the components of the smooth part of the
special fiber and that on the connecting annuli the differences of these
Coleman integrals form a harmonic cochain on the edges of the dual graph of the
special fiber. This determines the Vologodsky integral completely. We analyze
the behavior of the integral on the connecting annuli and we explain the
results in the case of a Tate elliptic curve.

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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: physics