Manuel Saorin (Murcia), Derived equivalence induced by non-compact tilting sets.

Abstract:

Since the seminal papers of Rickard and Keller on Morita theory for triangulated categories it is known that if $T$ is a compact tilting complex in the derived category of a ring $A$, then the t-structure in $\mathcal{D}(A)$ generated by $T$ has a heart $\mathcal{H}$ which is equivalent to the module category over $B=End_{\mathcal{D}(R)}(T)$. Moreover, in that case there is a triangulated equivalence $\mathcal{D}(\mathcal{H})\stackrel{\cong}{\longrightarrow}\mathcal{D}(R)$ whose restriction to $\mathcal{H}$ is naturally isomorphic to the inclusion functor $\mathcal{H}\hookrightarrow\mathcal{D}(R)$. In this talk we will present an extension of this result to non-compact tilting object in any compactly generated algebraic triangulated category.