Noetherian local ring with non-lci formal fibers

Question

I am looking for an example of a noetherian local ring $A$ such that its formal fibers are not complete intersection rings in the sense of https://stacks.math.columbia.edu/tag/09PY (i.e., there is a prime ideal $\mathfrak{p}\subset A$ such that the ring $k(\mathfrak{p}) \otimes_A \widehat{A}$ is not a complete intersection ring).

I assume that there should be a classical reference for such example, but I cannot find it online.

P.S. I would appreciate a lot an example that is "easy to digest" (if such exists at all).

P.S.2 Clearly, any such ring cannot be an excellent ring. However, a classical example of a non-excellent DVR does have lci formal fibers, so this example does not work.

Answer 1

Ferrand and Raynaud constructed a 1-dimensional Noetherian local domain $A$ such that $\operatorname{Frac}(A) \otimes_A \hat{A}$ is not Gorenstein. In particular, since local complete intersection rings are Gorenstein, their example is a Noetherian local ring with non-lci generic formal fiber. See Proposition 3.1 and Remarque 3.2(i) in

Daniel Ferrand and Michel Raynaud, "Fibres formelles d'un anneau local noethérien," Ann. Sci. École Norm. Sup. (4) 3 (1970), 295–311; MR 272779; DOI 10.24033/asens.1195.