Let k be a field of characteristic zero and P(V) a projective space over kwith homogeneous coordinate ring Sym•(V∗). The classical Bernstein-Gelfand-Gelfand correspondence (cf. [3]) interprets the derived category of coherent sheaves on P in terms of modules over the exterior algebra Λ•(V). This result was later generalized by Kapranov [8], who considered a complete intersection X ⊂ P of quadrics given by polynomials W1, . . . ,Wm ∈ Sym2(V∗). By a theorem of Serre, coherent sheaves on such X can be described in terms of graded modules over SW = Sym •(V∗)/〈W1, . . . ,Wm〉, where 〈W1, . . . ,Wm〉 is the homogenous ideal generated by W1, . . . ,Wm. In this situation, the exterior algebra Λ•(V) is replaced by the graded Clifford algebra Cl(W1, . . . ,Wm) generated by elements ŷ0, . . . , ŷn of degree 1 and central elements z1, . . . , zm of degree 2, subject to relations