Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Retract rationality and algebraic tori   For any prime number $p$ and field $k$, we characterize the $p$-retract
rationality of an algebraic $k$-torus in terms of its character lattice. We
show that a $k$-torus is retract rational if and only if it is $p$-retract
rational for every prime $p$, and that the Noether problem for retract
rationality for a group of multiplicative type $G$ has an affirmative answer
for $G$ if and only if the Noether problem for $p$-retract rationality for $G$
have a positive answer for all $p$. For every finite set of primes $S$ we give
examples of tori that are $p$-retract rational if and only if $p\notin S$.

27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th