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Algebraic properties of Witt vectors $W(K^{\flat\circ})$, $K$ a characteristic 0 perfectoid ...

Let $K$ be as in the title with tilt $K^\flat$. $W = W(K^{\circ\flat})$ satisfies a universal property: it is the unique $p$-adically complete $p$-torsion free $\mathbb{Z}_p$-algebra $A$ with $A / pA …