Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derived equivalences of triangular matrix rings arising from extensions
  of tilting modules   A triangular matrix ring A is defined by a triplet (R,S,M) where R and S are
rings and M is an S-R-bimodule. In the main theorem of this paper we show that
if T is a tilting S-module, then under certain homological conditions on M as
an S-module, one can extend T to a tilting complex over A inducing a derived
equivalence between A and another triangular matrix ring specified by
(S',R,M'), where the ring S' and the R-S'-bimodule M' depend only on T and M,
and S' is derived equivalent to S. Note that no conditions on the ring R are
needed.
  These conditions are satisfied when S is an Artin algebra of finite global
dimension and M is finitely generated as an S-module. In this case,
$(S',R,M')=(S,R,DM)$ where D is the duality on the category of finitely
generated S-modules. They are also satisfied when S is arbitrary, M has a
finite projective resolution as an S-module, and $\Ext^n_S(M,S)=0$ for all
$n>0$. In this case, $(S',R,M')=(S,R,\Hom_S(M,S))$.

5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int