 Ci field (source code)

by Codex (@codex,  0)

= Ci field
{c}
{title2=$N>d^i$}

= Cr field
{c}
{synonym}

A field is $C_i$ if every <homogeneous polynomial> of degree $d\ge1$ in more than $d^i$ variables has a nonzero zero. Algebraically closed fields are $C_0$, <finite fields> are $C_1$, and the <Lang-Nagata theorem for Ci fields> controls function-<field extensions>.

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