Derived Morita equivalence of associative algebras
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An associative algebra $A$ is said to be Morita equivalent to another one $B$ if there is an equivalence $$mathsfMod_Asimeq mathsfMod_B$$ between its corresponding abelian categories of modules. Moreover, whenever $A$ and $B$ are commutative, they are Morita equivalent iff they are isomorphic. On the other hand, we say that $A$ is derived Morita equivalent to $B$ if there is an equivalence $$D(A)simeq D(B)$$ between its triangulated derived categories. My question is:
Q. If $A$ is commutative and derived Morita equivelent to $B$, is $A$ Morita equivalent to $B$?
homological-algebra derived-categories derived-algebraic-geometry
asked Aug 29 at 6:28
Enrique Becerra
24328
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up vote
5
down vote
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An associative algebra $A$ is said to be Morita equivalent to another one $B$ if there is an equivalence $$mathsfMod_Asimeq mathsfMod_B$$ between its corresponding abelian categories of modules. Moreover, whenever $A$ and $B$ are commutative, they are Morita equivalent iff they are isomorphic. On the other hand, we say that $A$ is derived Morita equivalent to $B$ if there is an equivalence $$D(A)simeq D(B)$$ between its triangulated derived categories. My question is:
Q. If $A$ is commutative and derived Morita equivelent to $B$, is $A$ Morita equivalent to $B$?
homological-algebra derived-categories derived-algebraic-geometry
asked Aug 29 at 6:28
Enrique Becerra
24328
add a comment |Â
up vote
5
down vote
favorite
up vote
5
down vote
favorite
An associative algebra $A$ is said to be Morita equivalent to another one $B$ if there is an equivalence $$mathsfMod_Asimeq mathsfMod_B$$ between its corresponding abelian categories of modules. Moreover, whenever $A$ and $B$ are commutative, they are Morita equivalent iff they are isomorphic. On the other hand, we say that $A$ is derived Morita equivalent to $B$ if there is an equivalence $$D(A)simeq D(B)$$ between its triangulated derived categories. My question is:
Q. If $A$ is commutative and derived Morita equivelent to $B$, is $A$ Morita equivalent to $B$?
homological-algebra derived-categories derived-algebraic-geometry
asked Aug 29 at 6:28
Enrique Becerra
24328
An associative algebra $A$ is said to be Morita equivalent to another one $B$ if there is an equivalence $$mathsfMod_Asimeq mathsfMod_B$$ between its corresponding abelian categories of modules. Moreover, whenever $A$ and $B$ are commutative, they are Morita equivalent iff they are isomorphic. On the other hand, we say that $A$ is derived Morita equivalent to $B$ if there is an equivalence $$D(A)simeq D(B)$$ between its triangulated derived categories. My question is:
Q. If $A$ is commutative and derived Morita equivelent to $B$, is $A$ Morita equivalent to $B$?
homological-algebra derived-categories derived-algebraic-geometry
homological-algebra derived-categories derived-algebraic-geometry
asked Aug 29 at 6:28
Enrique Becerra
24328
asked Aug 29 at 6:28
Enrique Becerra
24328
asked Aug 29 at 6:28
Enrique Becerra
24328
asked Aug 29 at 6:28
Enrique Becerra
24328
asked Aug 29 at 6:28
Enrique Becerra
24328
24328
add a comment |Â
add a comment |Â
1 Answer
1
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votes
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5
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This seems to be true by https://arxiv.org/pdf/math/9810134.pdf , theorem 2.7.
answered Aug 29 at 6:44
Mare
2,4662926
cambridge.org/core/journals/… for non-pdf version
– AHusain
Aug 29 at 6:57
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
5
down vote
accepted
This seems to be true by https://arxiv.org/pdf/math/9810134.pdf , theorem 2.7.
answered Aug 29 at 6:44
Mare
2,4662926
cambridge.org/core/journals/… for non-pdf version
– AHusain
Aug 29 at 6:57
add a comment |Â
up vote
5
down vote
accepted
This seems to be true by https://arxiv.org/pdf/math/9810134.pdf , theorem 2.7.
answered Aug 29 at 6:44
Mare
2,4662926
cambridge.org/core/journals/… for non-pdf version
– AHusain
Aug 29 at 6:57
add a comment |Â
up vote
5
down vote
accepted
up vote
5
down vote
accepted
This seems to be true by https://arxiv.org/pdf/math/9810134.pdf , theorem 2.7.
answered Aug 29 at 6:44
Mare
2,4662926
This seems to be true by https://arxiv.org/pdf/math/9810134.pdf , theorem 2.7.
answered Aug 29 at 6:44
Mare
2,4662926
answered Aug 29 at 6:44
Mare
2,4662926
answered Aug 29 at 6:44
Mare
2,4662926
answered Aug 29 at 6:44
Mare
2,4662926
2,4662926
cambridge.org/core/journals/… for non-pdf version
– AHusain
Aug 29 at 6:57
add a comment |Â
cambridge.org/core/journals/… for non-pdf version
– AHusain
Aug 29 at 6:57
cambridge.org/core/journals/… for non-pdf version
– AHusain
Aug 29 at 6:57
cambridge.org/core/journals/… for non-pdf version
– AHusain
Aug 29 at 6:57
add a comment |Â
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