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The Stacks project

Definition 15.115.1. Let A \to B be an extension of discrete valuation rings with fraction fields K \subset L.

  1. We say a finite field extension K_1/K is a weak solution for A \subset B if all the extensions (A_1)_{\mathfrak m_ i} \subset (B_1)_{\mathfrak m_{ij}} of Remark 15.114.1 are weakly unramified.

  2. We say a finite field extension K_1/K is a solution for A \subset B if each extension (A_1)_{\mathfrak m_ i} \subset (B_1)_{\mathfrak m_{ij}} of Remark 15.114.1 is formally smooth in the \mathfrak m_{ij}-adic topology.

We say a solution K_1/K is a separable solution if K_1/K is separable.


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