Determination of Quadratic Lattices by Local Structure and Sublattices of Codimension One
For definite quadratic lattices over the rings of integers of algebraic number fields, it is shown that lattices are determined up to isometry by their local structure and sublattices of codimension 1. In particular, a theorem of Yoshiyuki Kitaoka for $\mathbb{Z}$-lattices is generalized to definit...
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| Format: | Others |
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OpenSIUC
2015
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| Online Access: | https://opensiuc.lib.siu.edu/dissertations/1026 https://opensiuc.lib.siu.edu/cgi/viewcontent.cgi?article=2030&context=dissertations |
| Summary: | For definite quadratic lattices over the rings of integers of algebraic number fields, it is shown that lattices are determined up to isometry by their local structure and sublattices of codimension 1. In particular, a theorem of Yoshiyuki Kitaoka for $\mathbb{Z}$-lattices is generalized to definite lattices over algebraic number fields. |
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