All Questions
Tagged with derived-categories differential-graded-algebras
13 questions with no upvoted or accepted answers
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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 ...
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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
$$ ...
- 40.2k
4
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240
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Derived category of dg modules vs. graded modules over a formal dg-algebra
Let $R = \oplus_{i\geq0} R_i$, $R_0 = k$ ($k$ a field) be a positively-graded commutative noetherian algebra, regarded as an augmented dg-algebra with zero differential.
Depending on one's interest, ...
- 471
4
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detecting a semi-free module from its bar-resolution
Let $A$ be a DG-algebra over a field (say $k$). A DG-module $M$ over $A$ is said to be semi-free if it admits an exhaustive filtration $0 = M_0 \subset M_1 \subset \ldots \subset M_p = M$ such that ...
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4
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Does derived equivalence imply dg Morita equivalence between DG algebras over field with char$=0$?
Let $A$, $B$ be two DG algebras and $D(A)$, $D(B)$ be derived categories of DG-modules of $A$, $B$, respectively. We call $A$ and $B$ are dg Morita equivalent if there is an $A$-$B$ bimodule $T$ with ...
- 9,019
4
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Formal DG-algebras
Sorry for this question but I really have difficulties with model categories.
Usually a $dg$-algebra $A$ is called formal, if there exists a $dg$-algebra $B$ and quasi-isomorphisms $$A\leftarrow B\to ...
- 2,554
3
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Natural transformation and Hochschild cohomology
I am reading the lecture note by Căldăraru:https://arxiv.org/pdf/math/0501094, in the last chapter of this note, he said that we should consider dg category instead of the derived category of coherent ...
- 395
3
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proper smooth dg-categories and colimit
Let $I$ be a filtered category and $\{k_i\}_{i\in I}$ be a system of commutative rings over $I$. Toen proved that there is an equivalence of categories
$$
\text{Colim}-\otimes^{\mathbb{L}}_{k_i} k:\...
- 349
2
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dg-natural transformation between FM functors and Hom between kernels
The question is related to Morphism between Fourier-Mukai functors implies the morphism between kernels?
Consider a complex smooth projective variety $X$ and the bounded derived category $D^b(X)$, it ...
anon
2
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When is $C\text-\mathsf{dg\text-mod}$ determined by the connective base changes?
I'm using cohomological gradings.
For $C\in k\text-\mathsf{cdga}$ (where $k$ can be taken of characteristic 0), a morphism $C\to A$ to a connective dg-algebra $A\in k\text-\mathsf{cdga}_{\leq0}$ ...
- 283
1
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72
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Bound on Hochschild dimension of a dg-algebra
Consider a dg-algebra $A$, is there any way I can estimate the Hochschild dimension, or global dimension of $A$?
More precisely the algebra that I am considering is the Endomorphism dg-algebra $\...
- 213
1
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Does a homologically bounded dg A-module admit a "locally finite" semi-free resolution
Let $A$ be a bounded dg-algebra whose underlying algebra is Noetherian and such that $H^*(A)$ is Noetherian. Let $M$ be a cohomologically bounded dg-module over $A$, whose cohomology groups are ...
- 101
0
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Is the inverse of the criterion of fully-faithfulness of derived tensor product also true?
Let $A$ and $B$ be differential graded algebras over a field $k$ and $D(A)$ and $D(B)$ be the derived categories of differential graded modules.
Let $N$ be an $A$-$B$ bimodule. Then $(-)\otimes^{\...
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