Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the semistability of binary forms over number fields   Let $K$ be a number field, ${\mathcal O}_K$ its ring of integers, and $f(x,
y) \in {\mathcal O}_K[x, y]$ a binary form with integer coefficents. For any
given prime $p \in {\mathcal O}_K$ we determine explicitly a binary form $g$
(resp. $\bar f$), $\mbox{GL}_2 (K)$-equivalent to $f$ which is semistable over
the local field $K_p$ (resp. the global field $K$). Moreover, if $\xi(f) $ is
the corresponding moduli point in the weighted projective space
${\mathbb{WP}}_{\mathbf w}^n (K)$ for a strictly semistable binary form $f$, we
determine the weighted moduli height $\mathfrak{h} (\xi(f))$ for $d=4, 6, 8,
10$.

34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
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The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg