Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local Solubility of Hyperelliptic Curves   We give a condition for a hyperelliptic curve $C$ over a local field $K$ to
be locally soluble, on the condition that $C$ obtains semistable reduction
after a tame extension of $K$, and that the residue field $k$ is sufficiently
large relative to the genus of the curve. The condition is presented in terms
of the cluster picture of $C$, a combinatorial object which determines much of
the local arithmetic of $C$.

31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom