Consider torsion-free modules over the germ of a fixed isolated algebraic hypersurface singularity $\{f=0\}\subset\mathbb{C}^n$.
There are natural functors: 

modules over $\mathbb{C}[x_1,..,x_n]/(f)$--> modules over $\mathbb{C}\{x_1,..,x_n\}/(f)$-->  modules over $\mathbb{C}[[x_1,..,x_n]]/(f)$.

Are they faithful, surjective? I know they are not surjective for an arbitrary local ring, but isolated hypersurface singularity is quite special.