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- W4297067557 abstract "Let $mathcal{O}$ be an order of index $m$ in the maximal order of a quadratic number field $k=mathbb{Q}(sqrt{d})$. Let $underline{mathbf{O}}_{d,m}$ be the orthogonal $mathbb{Z}$-group of the associated norm form $q_{d,m}$. We describe the structure of the pointed set $H^1_{mathrm{fl}}(mathbb{Z},underline{mathbf{O}}_{d,m})$, which classifies quadratic forms isomorphic (properly or improperly) to $q_{d,m}$ in the flat topology. Gauss classified quadratic forms of fundamental discriminant and showed that the composition of any binary $mathbb{Z}$-form of discriminant $Delta_k$ with itself belongs to the principal genus. Using cohomological language, we extend these results to forms of certain non-fundamental discriminants." @default.
- W4297067557 created "2022-09-26" @default.
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- W4297067557 date "2017-02-16" @default.
- W4297067557 modified "2023-10-16" @default.
- W4297067557 title "On the flat cohomology of binary norm forms" @default.
- W4297067557 doi "https://doi.org/10.48550/arxiv.1702.05080" @default.
- W4297067557 hasPublicationYear "2017" @default.
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