Parametrizing quartic algebras over an arbitrary base

  title={Parametrizing quartic algebras over an arbitrary base},
  author={M. Wood},
  journal={arXiv: Number Theory},
  • M. Wood
  • Published 2010
  • Mathematics
  • arXiv: Number Theory
  • We parametrize quartic commutative algebras over any base ring or scheme (equivalently finite, flat degree four $S$-schemes), with their cubic resolvents, by pairs of ternary quadratic forms over the base. This generalizes Bhargava's parametrization of quartic rings with their cubic resolvent rings over $\mathbb{Z}$ by pairs of integral ternary quadratic forms, as well as Casnati and Ekedahl's construction of Gorenstein quartic covers by certain rank 2 families of ternary quadratic forms. We… CONTINUE READING
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