All Questions

Let $k$ be a field and let $A$ and $B$ be finite-dimensional selfinjective $k$-algebras. Suppose we have an isomorphism of homotopy categories $F: K^b(A-mod) \cong K^b(B-mod)$ that descends to a ...

I've been reading about connections between Coxeter groups and preprojective algebras, and I keep running into two operations on the derived categories of preprojective algebras which seem very ...

This is a question on geometric tilting theory. On smooth projective variety it is possible to define in general tilting object as perfect complex that satisfy some properties, but are there examples ...

I suppose that Beilinson's compact generator (and, in fact, tilting object) $\mathcal{O} \oplus \mathcal{O}(1)$ in $D(\mathbb{P}^1)$ is the most well known example. I have the following simple ...

Let $X$ be a smooth projective variety over a field, than tilting object $T$ on $X$ is a perfect complex that is a compact generator of the derived category $\operatorname{D}(QCoh(X))$ and satisfies ...