Lemma 16.7.3. Let $R$ be a Noetherian ring. Let $\Lambda $ be an $R$-algebra. Let $\pi \in R$ and assume that $\text{Ann}_ R(\pi ) = \text{Ann}_ R(\pi ^2)$ and $\text{Ann}_\Lambda (\pi ) = \text{Ann}_\Lambda (\pi ^2)$. Let $A \to \Lambda $ be an $R$-algebra map with $A$ of finite presentation and assume $\pi $ is strictly standard in $A$ over $R$. Let

be a factorization with $\bar C$ of finite presentation. Then we can find a factorization $A \to B \to \Lambda $ with $B$ of finite presentation such that $R_\pi \to B_\pi $ is smooth and such that

## Comments (0)