Lemma 23.8.8. Let $S$ be a finite type algebra over a field $k$.

for a prime $\mathfrak q \subset S$ the local ring $S_\mathfrak q$ is a complete intersection in the sense of Algebra, Definition 10.133.5 if and only if $S_\mathfrak q$ is a complete intersection in the sense of Definition 23.8.5, and

$S$ is a local complete intersection in the sense of Algebra, Definition 10.133.1 if and only if $S$ is a local complete intersection in the sense of Definition 23.8.5.

## Comments (2)

Comment #1298 by Kestutis Cesnavicius on

Comment #1308 by Johan on