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KindShowingImportancePrizesTopicFargues–Fontaine curve1 result

The adic-space curve of Fargues–Fontaine, whose classical points parametrize the untilts to characteristic zero of a given perfectoid field; a central object of Scholze's p-adic Hodge theory and the relative Fargues–Fontaine curves for diamonds. Claims about the curve, its construction, its points, and untilts of perfectoid fields belong here; general p-adic or algebraic geometry claims not involv

A perfectoid field of characteristic p has infinitely many distinct untilts to characteristic zero, parametrized by the Fargues–Fontaine curve.
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Algebraic geometryimportance · settledImportance 0.12, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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