Koszul Duality for Coherent Sheaves

@misc{bouhada2026koszul,
  title = {{Koszul Duality for Coherent Sheaves}},
  author = {A. M. Bouhada},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.14299},
  eprint = {2607.14299},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.14299},
}

TY  - UNPB
TI  - Koszul Duality for Coherent Sheaves
AU  - A. M. Bouhada
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2607.14299
UR  - https://arxiv.org/abs/2607.14299
AB  - We establish a bounded derived Koszul duality for infinite-dimensional Koszul algebras and derive the corresponding singular Koszul duality. We then specialize this framework to two classes of Koszul algebras, namely quadratic monomial algebras and absolutely Koszul algebras satisfying an additional homological condition, for which the resulting dualities admit particularly well-behaved forms. As an application to algebraic geometry, let X⊆ ℙ_k^n be an arbitrary closed projective subscheme. We obtain a Koszul-dual description of the bounded derived category D^b (coh(X)), thereby yielding a BGG-type correspondence for arbitrary closed projective subschemes in projective space. As a second application, in noncommutative projective geometry, we consider generalized Artin--Schelter regular Koszul algebras Λ^! arising as Koszul duals of finite-dimensional self-injective Koszul algebras Λ. We show that D^b (qgr(Λ^!)) is triangulated equivalent to the bounded derived category of finite-dimensional modules over a finite-dimensional Koszul algebra of finite global dimension. This yields a Beilinson-type description of D^b (qgr(Λ^!)), extending the classical description of coherent sheaves on projective space to this noncommutative setting.
ER  -