Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Final remarks on local discriminants   We show how the ramification filtration on the maximal elementary abelian
p-extension (p prime) on a local number field of residual characteristic p can
be derived using only Kummer theory and a certain orthogonality relation for
the Kummer pairing, even in the absence of a primitive p-th root of 1; the case
of other local fields with finite residue fields was treated earlier. In all
cases, we compute the contribution of cyclic extensions to Serre's degree-$p$
mass formula.

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The categories of this paper are: physics
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an