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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 ...

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 ...

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....

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 ...

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:...