Anwesh Ray

Shapes of tame abelian number fields

The shape of a number field $K$ of degree $n\geq2$ is the similarity class of the lattice obtained by projecting $\mathscr{O}_K$ orthogonally away from the rational line in Minkowski space. It defines a point in the space of shapes of rank-$(n-1)$ lattices, $\mathscr{S}_{n-1}:=\mathrm{GL}_{n-1}(\mathbb{Z})\backslash \m...