Isogeny classes of cubic spaces

• Arthur Bik ^[1] ; Alessandro Danelon ^[2] ; Andrew Snowden ^[3]
  1. [1] Max Planck Institute for Mathematics in the Sciences

     Max Planck Institute for Mathematics in the Sciences

     Kreisfreie Stadt Leipzig, Alemania

     
  2. [2] Eindhoven University of Technology

     Eindhoven University of Technology

     Países Bajos

     
  3. [3] University of Michigan–Ann Arbor

     University of Michigan–Ann Arbor

     City of Ann Arbor, Estados Unidos

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 4, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01056-3
• Enlaces
  • Texto completo
• Resumen

  • 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 ℕ ∪ {∞}. In particular, the set of classes is discrete and (under the partial order of embedability) satisfies the descending chain condition.

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