Lemma 86.14.1. Let $A \to B$ be a morphism in $\textit{WAdm}^{Noeth}$ (Formal Spaces, Section 85.17). The following are equivalent:

$A \to B$ satisfies the equivalent conditions of Lemma 86.11.1 and there exists an ideal of definition $I \subset B$ such that $B$ is rig-smooth over $(A, I)$, and

$A \to B$ satisfies the equivalent conditions of Lemma 86.11.1 and for all ideals of definition $I \subset A$ the algebra $B$ is rig-smooth over $(A, I)$.

## Comments (0)