2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120183We improve Ottaviani's splitting criterion for vector bundles on a quadric hypersurface and obtain the equivalent of the result by Rao, Mohan Kumar and Peterson. Then we give the classification of rank 2 bundles without "inner" cohomology on Q_n (n>3). It surprisingly exactly agrees with the classification by Ancona, Peternell and Wisniewski of rank 2 Fano bundles.Algebraic Geometry14F05, 14J60text