Lemma 109.36.1. There exists a local ring $A$, a finite type ring map $A \to B$ and a prime $\mathfrak q$ lying over $\mathfrak m_ A$ such that $B_{\mathfrak q}$ is flat over $A$, and for any element $g \in B$, $g \not\in \mathfrak q$ the ring $B_ g$ is neither finitely presented over $A$ nor flat over $A$.

Proof. See discussion above. $\square$

There are also:

• 1 comment(s) on Section 109.36: Finite type, not finitely presented, flat at prime

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).