Parametrization of ideal classes in rings associated to binary forms

@article{Wood2010ParametrizationOI,
  title={Parametrization of ideal classes in rings associated to binary forms},
  author={Melanie Matchett Wood},
  journal={arXiv: Number Theory},
  year={2010}
}
  • M. Wood
  • Published 27 August 2010
  • Mathematics
  • arXiv: Number Theory
We give a parametrization of the ideal classes of rings associated to integral binary forms by classes of tensors in $\mathbb Z^2\tensor \mathbb Z^n\tensor \mathbb Z^n$. This generalizes Bhargava's work on Higher Composition Laws, which gives such parametrizations in the cases $n=2,3$. We also obtain parametrizations of 2-torsion ideal classes by symmetric tensors. Further, we give versions of these theorems when $\mathbb Z$ is replaced by an arbitrary base scheme $S$, and geometric… 
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Rings and ideals parameterized by binary n‐ic forms
  • M. Wood
  • Mathematics
    J. Lond. Math. Soc.
  • 2011
TLDR
This paper shows exactly what algebraic structures are parametrized by binary n-ic forms, and proves these parametrizations when any base scheme replaces the integers, and shows that the correspondences between forms and the algebraic data are functorial in the base scheme.
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