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Todo
edit- Remark on lemma 37.12.1 of https://stacks.math.columbia.edu/tag/02HW which gives an infinitesimal condition for infinitesimal lifting of local rings. The interpretation here is smooth deformations of local rings, whether they be around points, or subschemes, can be deformed around the scheme.
- Vakil gives an interesting discussion relating formally smooth, etale, and unramified maps to analytic geometry. Checkout https://math.stanford.edu/~vakil/0506-216/216class5152.pdf
- Add (counter-)examples found in the external links section