An algebraic immediate valuation ring extension of characteristic p>0 is a filtered union of complete intersection algebras of finite type.
Algebra and Geometry
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A mixed characteristic valuation ring is a filtered colimit of complete intersection Z-algebras if Γ/Z val(p) has no p-torsion and the ring is Henselian.
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Algebraic valuation ring extensions as limits of complete intersection algebras
An algebraic immediate valuation ring extension of characteristic p>0 is a filtered union of complete intersection algebras of finite type.
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Valuation rings of mixed characteristic as limits of complete intersection rings
A mixed characteristic valuation ring is a filtered colimit of complete intersection Z-algebras if Γ/Z val(p) has no p-torsion and the ring is Henselian.