Let R —> Λ be a ring map. Let I ⊂ R be an ideal. Assume that

- I is nilpotent,
- Λ/IΛ is a filtered colimit of smooth R/I-algebras, and
- R —> Λ is flat.

Then Λ is a colimit of smooth R-algebras. See Tag 07CM.

Let R —> Λ be a ring map. Let I ⊂ R be an ideal. Assume that

- I is nilpotent,
- Λ/IΛ is a filtered colimit of smooth R/I-algebras, and
- R —> Λ is flat.

Then Λ is a colimit of smooth R-algebras. See Tag 07CM.