Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: p-adic integration on bad reduction hyperelliptic curves   In this paper, we introduce an algorithm for computing p-adic integrals on
bad reduction hyperelliptic curves. For bad reduction curves, there are two
notions of p-adic integration: Berkovich-Coleman integrals which can be
performed locally; and abelian integrals with desirable number-theoretic
properties. By covering a bad reduction hyperelliptic curve by annuli and basic
wide open sets, we reduce the computation of Berkovich-Coleman integrals to the
known algorithms on good reduction hyperelliptic curves. These are due to
Balakrishnan, Bradshaw, and Kedlaya, and to Balakrishnan and Besser for regular
and meromorphic 1-forms on good reduction curves, respectively. We then employ
tropical geometric techniques due to the first-named author with Rabinoff and
Zureick-Brown to convert the Berkovich-Coleman integrals into abelian
integrals. We provide examples of our algorithm, verifying that certain abelian
integrals between torsion points vanish.

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The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
12
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: econ
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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th