Reading Scholze and Weinstein: "Berkeley lectures on p-adic geometry" in the proof of lemma 19.3.5 they use that the infinite-dimensional ball $B^\infty_{\mathbb{C}_p}$ is affinoid perfectoid. I don't understand why this holds true. In contrast, the usual one-dimensional unit ball $B_{\mathbb{C}_p}=Spa(\mathbb{C}_p<T>,O_{\mathbb{C}_p}<T>)$ is not perfectoid. Can someone explain?
2026-03-25 12:55:23.1774443323
Why is the infinite dimensional unit ball perfectoid?
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