Strong approximation and Hasse principle for integral quadratic forms over affine curves

We extend some parts of the representation theory for integral quadratic forms over the ring of integers of a number field to the case over the coordinate ring k [ C ] of an affine curve C over a general base field k . By using genus theory, we link the strong approximation property of certain spin groups to the Hasse principle for representations of integral quadratic forms over k [ C ] and derive several applications. In particular, we give an example where a spin group does not satisfy strong approximation.