Koszul Duality for Coherent Sheaves
arXiv:2607.14299
The paper develops a bounded derived Koszul duality theory for infinite‑dimensional Koszul algebras, specializes it to certain quadratic and absolutely Koszul algebras, and uses it to give a BGG‑type description of the derived category of coherent sheaves on projective schemes defined by commutative Koszul algebras.
Abstract
We establish a bounded derived Koszul duality for infinite-dimensional Koszul algebras, and we obtain the corresponding singular Koszul duality. We then apply this framework to two classes of Koszul algebras, namely quadratic monomial algebras and absolutely Koszul algebras satisfying an additional homological condition. For these classes, the general duality specializes to particularly well-behaved forms. As an application to algebraic geometry, let \(Î\) be a commutative noetherian Koszul algebra generated in degree \(1\), and let \(X=\operatorname{Proj}(Î)\). We obtain a Koszul-dual description of the bounded derived category \(\mathsf{D}^{b}\!\bigl(\operatorname{coh}(X)\bigr)\). This gives a BGG-type correspondence for projective schemes defined by commutative noetherian Koszul algebras.
28 pages. Version 2: We introduce the notion of the stabilization of a stable category and strengthen the main theorem concerning the bounded derived category of coherent sheaves. Further geometric applications and results will be developed in future work