Integral Springer Theorem for Quadratic Lattices under Base Change of Odd Degree
| Autor: | Hu, Yong, Liu, Jing, Xu, Fei |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | A quadratic lattice $M$ over a Dedekind domain $R$ with fraction field $F$ is defined to be a finitely generated torsion-free $R$-module equipped with a non-degenerate quadratic form on the $F$-vector space $F\otimes_{R}M$. Assuming that $F\otimes_{R}M$ is isotropic of dimension $\geq 3$ and that $2$ is invertible in $R$, we prove that a quadratic lattice $N$ can be embedded into a quadratic lattice $M$ over $R$ if and only if $S\otimes_{R}N$ can be embedded into $S\otimes_{R}M$ over $S$, where $S$ is the integral closure of $R$ in a finite extension of odd degree of $F$. As a key step in the proof, we establish several versions of the norm principle for integral spinor norms, which may be of independent interest. Comment: 32 pages |
| Databáze: | arXiv |
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