Strong approximation and Hasse principle for integral quadratic forms over affine curves
Volume 216 / 2024
Acta Arithmetica 216 (2024), 277-289
MSC: Primary 11E04; Secondary 11E25, 11E57, 20G35
DOI: 10.4064/aa240111-9-7
Published online: 20 November 2024
Abstract
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.
