Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the vanishing of theta invariant and a conjecture of Huneke and
  Wiegand   Huneke and Wiegand conjectured that, if $M$ is a finitely generated,
non-free, torsion-free module with rank over a one-dimensional Cohen-Macaulay
local ring $R$, then the tensor product of $M$ with its algebraic dual has
torsion. This conjecture, if $R$ is Gorenstein, is a special case of a
celebrated conjecture of Auslander and Reiten on the vanishing of self
extensions that stems from the representation theory of finite-dimensional
algebras.
  If $R$ is a one-dimensional Cohen-Macaulay ring such that $R=S/(f)$ for some
local ring $(S, \mathfrak{n})$, and a non zero-divisor $f \in \mathfrak{n}^2$
on $S$, we make use of Hochster's theta invariant and prove that such
$R$-modules $M$ which have finite projective dimension over $S$ satisfy the
proposed torsion condition of the conjecture. Along the way we give several
applications of our argument pertaining to torsion properties of tensor
products of modules.

35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys