59 citations · 371 across the 37 of their papers we have counts for
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Parametrization of ideal classes in rings associated to binary forms
Melanie Matchett Wood
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 gener…
Rings and ideals parametrized by binary n-ic forms
Melanie Matchett Wood
The association of algebraic objects to forms has had many important applications in number theory. Gauss, over two centuries ago, studied quadratic rings and ideals associated to…
Parametrizing quartic algebras over an arbitrary base
Melanie Matchett Wood
We parametrize quartic commutative algebras over any base ring or scheme (equivalently finite, flat degree four -schemes), with their cubic resolvents, by pairs of ternary quadr…
Gauss composition over an arbitrary base
Melanie Matchett Wood
The classical theorems relating integral binary quadratic forms and ideal classes of quadratic orders have been of tremendous importance in mathematics, and many authors have given…
Quartic rings associated to binary quartic forms
Melanie Matchett Wood
We give a bijection between binary quartic forms and quartic rings with a monogenic cubic resolvent ring, relating the rings associated to binary quartic forms with Bhargava's cubi…