Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Valuative characterization of central extensions of algebraic tori on
  Krull domains   For an algebraic torus $T$, the finite central extensions $G$ of $T$ are
characterized in terms of ramification theory of regular actions of $G$ on
Krull algebras over an algebraically closed base field $K$ of any
characteristic.

9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th