I would like to know if there are any results similar to Cohen`s classification of complete dvr's if we drop the completeness assumption. Take an equal characteristic discrete valuation ring $A$ with residue field $k$. When does follows that $A\cong k(t)$ ? I am aware of the counterexample A conjectural characterization of equal characteristic DVRs. I am asking about assumptions we can ask for to ensure this result. What about $A$ of characteristic $0$ or $k$ algebraically closed?
2026-03-26 07:41:29.1774510889
Classification of non-complete dvr's
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