Lemma 109.75.1. There exists a commutative ring $A$ and a flat $A$-algebra $B$ which cannot be written as a filtered colimit of finitely presented flat $A$-algebras. In fact, we may either choose $A$ to be a finite type $\mathbf{F}_ p$-algebra or a $1$-dimensional Noetherian local ring with residue field of characteristic $0$.

Proof. See discussion above. $\square$

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