Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Detecting Koszulness and related homological properties from the algebra
  structure of Koszul homology   Let $k$ be a field and $R$ a standard graded $k$-algebra. We denote by
$\operatorname{H}^R$ the homology algebra of the Koszul complex on a minimal
set of generators of the irrelevant ideal of $R$. We discuss the relationship
between the multiplicative structure of $\operatorname{H}^R$ and the property
that $R$ is a Koszul algebra. More generally, we work in the setting of local
rings and we show that certain conditions on the multiplicative structure of
Koszul homology imply strong homological properties, such as existence of
certain Golod homomorphisms, leading to explicit computations of Poincar\'e
series. As an application, we show that the Poincar\'e series of all finitely
generated modules over a stretched Cohen-Macaulay local ring are rational,
sharing a common denominator.

8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat