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Isogeny classes of cubic spaces
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abstract
A cubic space is a vector space equipped with a symmetric trilinear form. Two cubic spaces are isogeneous if each embeds into the other. A cubic space is non-degenerate if its form cannot be expressed as a finite sum of products of linear and quadratic forms. We classify non-degenerate cubic spaces of countable dimension up to isogeny: the isogeny classes are completely determined by an invariant we call the residual rank, which takes values in $\mathbf{N} \cup \{\infty\}$. In particular, the set of classes is discrete and (under the partial order of embedability) satisfies the descending chain condition.
Forward citations
Cited by 2 Pith papers
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