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arXiv · 2312.08849

Strong Approximation and Hasse Principle for Integral Quadratic Forms over Affine Curves

Yong Hu·Jing Liu·Yisheng Tian
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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 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.

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Yong Hu, Jing Liu, Yisheng Tian. 2023-12-14. Strong Approximation and Hasse Principle for Integral Quadratic Forms over Affine Curves. https://doi.org/10.4064/aa240111-9-7

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