Orientability of a p-adic Lie tower, the existence of a Galois-equivariant lift of its Sen operator, is exactly what makes the pro-analytic de Rham period ring a Galois-equivariant power series ring over the tower's locally analytic completion.
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de Rham theory and locally analytic vectors
Orientability of a p-adic Lie tower, the existence of a Galois-equivariant lift of its Sen operator, is exactly what makes the pro-analytic de Rham period ring a Galois-equivariant power series ring over the tower's locally analytic completion.