Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On an explicit reciprocity law in local class field theory via
  $(\varphi, \Gamma)$-modules   Let $K$ be an unramified extension of $\mathbb{Q}_2$ and $\mu_{2^n}$ the
group of $2^n$-th root of unity for a fixed integer $n\geqslant 2$. In this
paper, we give an explicit formula for the $\mu_{2^n}$-valued Hilbert symbol
over $K_n := K(\mu_{2^n})$ using the theory of $(\varphi, \Gamma)$-modules.

16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con