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1 vote
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full strong exceptional collection

I am wondering whether, if a triangulated category $\mathcal{D}$ has a full strong exceptional collection (infinite), it is triangle-equivalent to the bounded derived category of finitely generated ...
Paulo Rossi's user avatar
6 votes
0 answers
201 views

Smoothness of a variety implies homological smoothness of DbCoh

I have been told that $D^bCoh(X)$ is homologically smooth if $X$ is a smooth variety, and I am trying to construct a proof. My background is not in algebra, so I apologize for elementary questions. It ...
DbCohSmoothness's user avatar
5 votes
1 answer
262 views

Derived Morita equivalence of associative algebras

An associative algebra $A$ is said to be Morita equivalent to another one $B$ if there is an equivalence $$\mathsf{Mod}_A\simeq \mathsf{Mod}_B$$ between its corresponding abelian categories of modules....
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9 votes
0 answers
506 views

Categorification of definitions in the context of the derived category of quasi-coherent sheaves

Let $SpecA=X$ be an affine noetherian scheme. Let $QCoh(X)$ denote the derived (stable $\infty$-)category of quasi-coherent sheaves on $X$. There are the following special full subcategories spanned ...
Saal Hardali's user avatar
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3 votes
0 answers
111 views

Is there a relation between Projection formula and Verdier duality

For suitable settings, $f\colon X\to Y$, $F,G$ we have projection formula and Verdier duality: Projection formula: $Rf_!(F\otimes^\mathbb{L}f^{-1}G)\cong Rf_!F\otimes^{\mathbb{L}}G$ Verdier Duality:...
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