Lemma 10.134.9. Let $k$ be a field. Let $S$ be a finite type $k$-algebra. The following are equivalent:

The ring $S$ is a local complete intersection over $k$.

All local rings of $S$ are complete intersection rings over $k$.

All localizations of $S$ at maximal ideals are complete intersection rings over $k$.

## Comments (0)

There are also: