On the equality of de Rham depth and formal grade in characteristic zero

Abstract

Let $Y\subset {\mathbb{P}}_k^n$ be a non-singular proper closed subset of projective $n$-space over a field $k$ of characteristic zero and let $I\subset R=k[x_0,\dots ,x_n]$ be the homogeneous defining ideal of $Y$. We show that in this case, the de Rham depth of $Y$ is the same as the so-called formal grade of $I$ in $R$.

3 pages, any comment is welcome