Melanie Matchett Wood
Moduli Spaces for Rings and Ideals
I will talk about spaces whose points parametrize certain kinds of
orders in number fields, and ideal classes in those orders. The
spaces give concrete classifications of these number theoretic objects.
In particular, I will discuss the rings and ideals parametrized by binary
forms, and concrete moduli spaces for the ideal classes of these rings.
I will also discuss how we can understand these and other similar
parametrizations geometrically, and when the integers are replaced by
an arbitrary base scheme.