Lemma 10.159.10. Let $(R, \mathfrak m)$ be a Noetherian complete local ring. Assume $R$ is regular.

If $R$ contains either $\mathbf{F}_ p$ or $\mathbf{Q}$, then $R$ is isomorphic to a power series ring over its residue field.

If $k$ is a field and $k \to R$ is a ring map inducing an isomorphism $k \to R/\mathfrak m$, then $R$ is isomorphic as a $k$-algebra to a power series ring over $k$.

## Comments (2)

Comment #1853 by Matthieu Romagny on

Comment #1892 by Johan on