A decomposition `K ⊗[O] B ≃ ∏ᵢ Lᵢ` of the generic fibre ascends along an unramified extension `O → Oδ` (with `π` remaining a uniformizer) to `Kδ ⊗[Oδ] B ≃ ∏ᵢ Lᵢ`, compatibly with the `O`-structures.

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A decomposition `K ⊗[O] B ≃ ∏ᵢ Lᵢ` of the generic fibre ascends along an unramified extension `O → Oδ` (with `π` remaining a uniformizer) to `Kδ ⊗[Oδ] B ≃ ∏ᵢ Lᵢ`, compatibly with the `O`-structures. · Prove2Me