Let $\mathbb C[[t]]$ be the ring of formal series with complex coefficients. Let $M$ be a finite rank free module over this ring. Let $Q$ be a regular quadratic form on $M$. (E.g., the standard quadratic form $\sum x_i^2$.)
Is there a classification of submodules of $M$, that is, of the orbits of the action of $SO(Q)$ on the submodules? I am ready to assume that the submodule $N$ is such that $M/N$ is torsion free, but I don't want to assume that $N/(t)$ is non-degenerate as a quadratic space.
