The Stacks project

Situation 58.19.1. Let $(A, \mathfrak m)$ be a Noetherian local ring and $f \in \mathfrak m$. We set $X = \mathop{\mathrm{Spec}}(A)$ and $X_0 = \mathop{\mathrm{Spec}}(A/fA)$ and we let $U = X \setminus \{ \mathfrak m\}$ and $U_0 = X_0 \setminus \{ \mathfrak m\}$ be the punctured spectrum of $A$ and $A/fA$.