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Mar 29, 2021 at 0:05 comment added user267839 @abx: No, I not require that $A$ should have dimension $1$, for example $A$ could be an affine surface and $X$ the blowup of the closed point of $A$.
Mar 27, 2021 at 6:16 comment added abx So, you want your local ring $A$ of Krull dimension 1. And do you want $D$ to be Cartier, which probably means that $A$ should be a DVR?
Mar 27, 2021 at 2:07 history asked user267839 CC BY-SA 4.0