Deformation theory of orthogonal and symplectic sheaves

We show that the space of first-order deformations of an orthogonal (resp. symplectic) sheaf over a smooth projective scheme is the first hypercohomology space of a complex which is naturally constructed out of the orthogonal (resp. symplectic) sheaf. We also provide an obstruction theory of these objects whose target is the second hypercohomology space of this complex.