BGG correspondence
In mathematics, the Bernstein-Gelfand-Gelfand correspondence or BGG correspondence for short is the first example of the Koszul duality. Established by Joseph Bernstein, Israel Gelfand, and Sergei Gelfand, the correspondence is an explicit triangulated equivalence that relates the bounded derived category of coherent sheaves on the projective space P ( V ) {\displaystyle \mathbb {P} (V)} and the stable category of graded modules gr ∧ V {\displaystyle \operatorname {gr} \wedge V} over the exterior algebra ∧ V {\displaystyle \wedge V} ; i.e., D b ( P ( V ) ) ≃ gr ∧ V ¯ {\displaystyle D^{b}(\mathbb {P} (V))\simeq {\overline {\operatorname {gr} \wedge V}}} .