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What examples of abelian categories $\mathcal{A}$ are there such that the derived category $\mathcal{D}(\mathcal{A})$ can be described concretely? For example, is there a concrete way of describing $\...

Let $G$ be a finite group. Let $p$ be a prime dividing $|G|$. Let $k:=\overline{\mathbb{F}_p}$. Let $b$ be a $p$-block of $kG$ with abelian defect group $D$. Let $H:=N_G(D)$. Let $c$ be the Brauer ...

Let $G$ be a finite group. Let $p$ be a prime dividing $|G|$. Let $K:=\overline{\mathbb{F}_p}$. Let $b$ be a $p$-block of $G$ with abelian defect group $D$. Let $H:=N_G(D)$. Let $c$ be the Brauer ...

Let $G$ be a finite group and $\mathcal{A}$ be a $dg$-algebra. Assume $G$ acts on $\mathcal{A}$, i.e. there exists a homomorphism $G\to {\rm Aut}_{dg}(\mathcal{A})$. Assume further there exists a $dg$...

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 ...