Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An approach to the finitistic dimension conjecture   Let $R$ be a finite dimensional $k$-algebra over an algebraically closed
field $k$ and $\mathrm{mod} R$ be the category of all finitely generated left
$R$-modules. For a given full subcategory $\mathcal{X}$ of $\mathrm{mod} R,$ we
denote by $\pfd \mathcal{X}$ the projective finitistic dimension of
$\mathcal{X}.$ That is, $\pfd \mathcal{X}:=\mathrm{sup} \{\pd X :
X\in\mathcal{X} \text{and} \pd X<\infty\}.$ \
  It was conjectured by H. Bass in the 60's that the projective finitistic
dimension $\pfd (R):=\pfd (\mathrm{mod} R)$ has to be finite. Since then, much
work has been done toward the proof of this conjecture. Recently, K. Igusa and
J. Todorov defined a function $\Psi:\mathrm{mod} R\to \Bbb{N},$ which turned
out to be useful to prove that $\pfd (R)$ is finite for some classes of
algebras. In order to have a different approach to the finitistic dimension
conjecture, we propose to consider a class of full subcategories of
$\mathrm{mod} R$ instead of a class of algebras, namely to take the class of
categories $\F(\theta)$ of $\theta$-filtered $R$-modules for all stratifying
systems $(\theta,\leq)$ in $\mathrm{mod} R.$

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The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph