  The space of $n \times m$ complex matrices can be regarded as an algebraic
variety on which the group ${\bf GL}_n \times {\bf GL}_m$ acts. There is a rich
interaction between geometry and representation theory in this example. In an
important paper, de Concini, Eisenbud, and Procesi classified the equivariant
ideals in the coordinate ring. More recently, we proved a noetherian result for
families of equivariant modules as $n$ and $m$ vary. In this paper, we
establish analogs of these results for the space of $(n|n) \times (m|m)$ queer
matrices with respect to the action of ${\bf Q}_n \times {\bf Q}_m$, where
${\bf Q}_n$ denotes the queer supergroup. Our work is motivated by connections
to the Brauer category and the theory of twisted commutative algebras.
