Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Torsion pairs and filtrations in abelian categories with tilting objects   Given a noetherian abelian category $\mathcal Z$ of homological dimension two
with a tilting object $T$, the abelian category $\mathcal Z$ and the abelian
category of modules over $\text{End} (T)^{\textit{op}}$ are related by a
sequence of two tilts; we give an explicit description of the torsion pairs
involved. We then use our techniques to obtain a simplified proof of a theorem
of Jensen-Madsen-Su, that $\mathcal Z$ has a three-step filtration by
extension-closed subcategories. Finally, we generalise Jensen-Madsen-Su's
filtration to a noetherian abelian category of any finite homological
dimension.

11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
9
The categories of this paper are: nlin