Arithmetic Springer theorem and $n$-universality under field extensions

Zilong He

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arXiv · 2312.09560

Arithmetic Springer theorem and $n$-universality under field extensions

Zilong He

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Abstract

Based on BONGs theory, we prove the norm principle for integral and relative integral spinor norms of quadratic forms over general dyadic local fields, respectively. By virtue of these results, we further establish the arithmetic version of Springer's theorem for indefinite quadratic forms. Moreover, we solve the lifting problems on $n$-universality over arbitrary local fields.

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Zilong He. 2025-04-18. Arithmetic Springer theorem and $n$-universality under field extensions. https://arxiv.org/abs/2312.09560

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