All Questions
Tagged with derived-categories ra.rings-and-algebras
8 questions with no upvoted or accepted answers
10
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Reconstruction of commutative differential graded algebras
Let $k$ be an algebraically closed field of characteristic $0$.
Let $A,B$ be commutative differential graded algebras (cdga) over $k$ such that $H^{i}(A)=H^{i}(B) =0 \ (i>0)$.
Here, differentials ...
- 889
10
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Has anyone seen this construction of dg algebras?
Let $A$ be an associative algebra, $M$ a right $A$-module. Suppose we are given an $A$-module homomorphism $M \to A$. Then we can make $M$ itself into an associative algebra via the multiplication
$$ ...
- 40.3k
8
votes
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flatness and derived completion
Let $A$ be a local ring of maximal ideal $\mathfrak{m}$. Let $\hat{A}$ be its completion.
If $A$ is noetherian , then we know that $A\rightarrow\hat{A}$ is faithfully flat.
If $A$ is not noetherian, ...
- 3,472
4
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Serre duality graded singularity category
Let $R$ be a local Gorenstein ring of Krull dimension $d$ with an isolated singularity. Defined $D_{sing}(R)$ as the Verdier quotient $D^b(R)/Perf(R)$). Then, a famous result of Auslander says that ...
- 7,320
4
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Formal DG-algebras
Sorry for this question but I really have difficulties with model categories.
Usually a $dg$-algebra $A$ is called formal, if there exists a $dg$-algebra $B$ and quasi-isomorphisms $$A\leftarrow B\to ...
- 2,554
2
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Restriction of scalars from an Azumaya algebra and preservation of perfect/compact objects of the derived categories
An Azumaya variety over a field is by definition a pair $(X,\mathcal A_X)$, where $X$ is an algebraic variety of finite type over that field and $\mathcal A_X$ is a sheaf of Azumaya algebras, namely ...
- 2,079
2
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injective dimension of dualizing complex
Let $R$ be a balanced dualizing complex of a Noetherian connected graded algebras $A$. Dose one always have $\text{id}_A R = \text{id}_{A^{op}} R$?
Thanks a lot.
- 141
1
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Pseudo-coherent complexes over sheaves of non-commutative rings
I am posing a question on derived categories to which I was not able to find an answer anywhere in the literature. I would appreciate any answer, hint or suggestion.
Assume that $\mathcal{R}_X$ is a ...
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