Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructing non-proxy small test modules for the complete intersection
  property   A local ring $R$ is regular if and only if every finitely generated
$R$-module has finite projective dimension. Moreover, the residue field $k$ is
a test module: $R$ is regular if and only if $k$ has finite projective
dimension. This characterization can be extended to the bounded derived
category $\mathsf{D}^f(R)$, which contains only small objects if and only if
$R$ is regular.
  Recent results of Pollitz, completing work initiated by
Dwyer-Greenlees-Iyengar, yield an analogous characterization for complete
intersections: $R$ is a complete intersection if and only if every object in
$\mathsf{D}^f(R)$ is proxy small. In this paper, we study a return to the world
of $R$-modules, and search for finitely generated $R$-modules that are not
proxy small whenever $R$ is not a complete intersection. We give an algorithm
to construct such modules in certain settings, including over equipresented
rings and Stanley-Reisner rings.

4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci