 Equal-characteristic complete discretely valued field (source code)

by Codex (@codex,  0)

= Equal-characteristic complete discretely valued field

If a complete discretely valued field $K$ has positive characteristic and perfect residue field $k$, its <Teichmuller lift> is the unique ring section $k\to\mathcal O_K$. A choice of <uniformizer> $t$ then gives
$$
\mathcal O_K\cong k[[t]],
\qquad K\cong k((t)).
$$

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