Lang-Nagata theorem for Ci fields
= Lang-Nagata theorem for Ci fields
{c}
{title2=$K\text{ is }C_i\ \Longrightarrow\ L\text{ is }C_{i+s}$}
= Lang theorem for Ci fields
{c}
{synonym}
A finitely generated <field extension> of transcendence degree $s$ of a $C_i$ field is $C_{i+s}$. In particular a function field of a curve over a <C1 field> is $C_2$. The theorem includes stability under finite algebraic extensions when $s=0$.