# what is the connection between D-modules and coordinate bundles?

Fix $n$ and a field $k$ of characteristic zero. Let $G$ be the pro-algebraic group of automorphims of $k[[x_1,...x_n]]$. Let $G_0$ be the subgroup of automorphisms preserving the closed point (note that for general $T$, $G_0(T)$ can be a proper subgroup of $G(T)$). Let $X$ be a regular variety over $k$ and let $P$ be the principal $G$ bundle of formal coordinate systems, naturally a $G$ torsor over $X$. I hear that there is a connection between $P$ and $D_X$-modules. what is this connection?

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@Sergiy: you removed a pair of brackets, turning $k[[x_1.\dots.x_n]]$ into $k[x_1, \dots, x_n]$, which is a rather differet thing! You should undo that change. –  Mariano Suárez-Alvarez Oct 10 '13 at 16:31