let $k$ be a finite field and $K=k[t]$ be the function field in one variable. Show that a non-trivial, non-Archimedean absolute value $\|\cdot\|$ on K is equivalent to $|\cdot|_{\mathbb{P}}$ for some prime ideal $\mathbb{P}$, generated by a monic irreducible polynomial $p(t) \in k[t]$.
2026-03-24 20:30:26.1774384226
Equivalence between valuations
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