2023/12/14 by Yong Hu, Jing Liu, Hu, Yong +3
Computer Science · Mathematics · #11E04 11E25 11E57 20G35 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2312.08849
openalex publication_date 2023/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 the 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.