Geodesic
On the derived category and $K$-functor of coherent sheaves on intersections of quadrics
Izvestiya. Mathematics , Tome 32 (1989) no. 1, pp. 191-204.

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A graded Clifford algebra connected with the complete intersection of several quadrics is considered. In terms of modules over this algebra, a description is given of the derived category of coherent sheaves and the Quillen $K$-functor of the intersection of quadrics, which generalizes the results of I. N. Bernshtein, I. M. Gel'fand, S. I. Gel'fand, and R. G. Swan. Here, ramified two-sheeted coverings of the parameter space arise in a natural way, the consideration of which is traditional for intersections of two or three quadrics. Bibliography: 12 titles. 
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M. M. Kapranov. On the derived category and $K$-functor of coherent sheaves on intersections of quadrics. Izvestiya. Mathematics , Tome 32 (1989) no. 1, pp. 191-204. http://geodesic.mathdoc.fr/item/IM2_1989_32_1_a9/

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