This paper is an elaboration of my lecture at the conference. The purpose is to explain how the Fargues–Fontaine curve and its decomposition into a punctured curve and the formal neighborhood of the puncture naturally appear from various forms of topological cyclic homology and maps between them. I make no claim of originality. My purpose here is to highlight some of the spectacular material contained in the papers of Nikolaus–Scholze [16], Bhatt–Morrow–Scholze [3], and Antieau–Mathew–Morrow–Nikolaus [1] on topological cyclic homology and in the book by Fargues–Fontaine [7] on their revolutionary curve.