Seminar

Reverse homological algebra deals with questions like the following ones, concerning a ring $R$ and a (left) $R$-module $k$: What $Ext_R(k,k)$-modules have the form $\mathrm{Ext}_R(M,k)$ for some $R$-module $M$? What are the essential images of the functor $\mathrm{RHom}_R(?,k)$ from various subcategories of the derived category of $R$-modules to the derived category of DG modules over $\mathrm{RHom}_R(k,k)$?

Some answers to the second question will be presented when $R$ is commutative, noetherian and local and $k$ is its residue field.
Under an additional hypothesis on $R$, which holds for complete intersections and for Golod rings, the first question will be answered "up to truncations." A crucial step of the proof involves a contravariant Koszul duality for (not necessarily commutative) connected DG algebras.

Part of the talk is based on joint work with David Jorgensen.