Loading…
Derived equivalence induced by infinitely generated -tilting modules
Let T R T_R be a right n n -tilting module over an arbitrary associative ring R R . In this paper we prove that there exists an n n -tilting module T R ′ T’_R equivalent to T R T_R which induces a derived equivalence between the unbounded derived category D ( R ) \mathcal {D}(R) and a triangulated s...
Saved in:
| Published in: | Proceedings of the American Mathematical Society 2011-12, Vol.139 (12), p.4225-4234 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Let
T
R
T_R
be a right
n
n
-tilting module over an arbitrary associative ring
R
R
. In this paper we prove that there exists an
n
n
-tilting module
T
R
′
T’_R
equivalent to
T
R
T_R
which induces a derived equivalence between the unbounded derived category
D
(
R
)
\mathcal {D}(R)
and a triangulated subcategory
E
⊥
\mathcal E_{\perp }
of
D
(
End
(
T
′
)
)
\mathcal {D}(\operatorname {End}(T’))
equivalent to the quotient category of
D
(
End
(
T
′
)
)
\mathcal {D}(\operatorname {End}(T’))
modulo the kernel of the total left derived functor
−
⊗
S
′
L
T
′
-\otimes ^{\mathbb L}_{S’}T’
. If
T
R
T_R
is a
classical
n
n
-tilting module
, we have that
T
=
T
′
T=T’
and the subcategory
E
⊥
\mathcal E_{\perp }
coincides with
D
(
End
|
(
T
)
)
\mathcal {D}(\operatorname {End}|(T))
, recovering the classical case. |
|---|---|
| ISSN: | 0002-9939 1088-6826 |
| DOI: | 10.1090/S0002-9939-2011-10900-6 |