Lemma 33.26.2. Let $X$ be a proper variety over $k$. Then

$K = H^0(X, \mathcal{O}_ X)$ is a field which is a finite extension of the field $k$,

if $X$ is geometrically reduced, then $K/k$ is separable,

if $X$ is geometrically irreducible, then $K/k$ is purely inseparable,

if $X$ is geometrically integral, then $K = k$.

## Comments (0)