Let $M$ be a regular holonomic $D_X$ module on a smooth complex variety $X$. The comparision theorem says that

$$RHom_{D_X}(M,\mathcal{O}_X)_x\cong RHom_{D_X,x}(M_x,\hat{\mathcal{O}}_{X,x}).$$ Now the very definition of $\hat{\mathcal{O}}_{X,x}$ suggests that there should also be objects $$RHom_{D_X,x}(M_x,\mathcal{O}_{X,x}/\mathfrak{m}_x^k),$$ for $k\geq 0$. However, $\mathcal{O}_{X,x}/\mathfrak{m}_x^k$ is not a $D_{X,x}$-module (or the zero module). Is there an interesting way to make sense of this expression?

Naively the outcome should be a (derived version) of just the set of truncated power series solutions the differential equations in $Ann_{D_X}M$.


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