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2 votes
0 answers
119 views

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 ...
user avatar
1 vote
0 answers
72 views

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 $\...
Felix's user avatar
  • 213
4 votes
0 answers
168 views

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 ...
Libli's user avatar
  • 7,300
7 votes
1 answer
288 views

Skew differential graded algebra

A sigma, or skew, derivation is a natural generalisation of the notion of derivation depending on an algebra automorphism $\sigma$ which when equal to $id = \sigma$ reduces to the usual notion of a ...
Jake Wetlock's user avatar
  • 1,144
1 vote
0 answers
46 views

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 ...
mathdonkey's user avatar
6 votes
1 answer
253 views

Is the hom in derived category of a dg-algebra compatible with base field extension?

Let $k$ be a field and $A$ be an ordinary $k$-algebra. Let $M$ and $N$ be two left $A$-modules then we could consider the Ext group $\mathrm{Ext}^i_A(M,N)$ which is actually a $k$-vector space. Let $l/...
Zhaoting Wei's user avatar
  • 9,019