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Tempered (adic) fundamental groups of hyperbolic curves and schemes over p-adic and adic base fields, including their dependence on the choice of geometric base-point and the special role of algebraically closed perfectoid base fields; central to anabelian reconstruction arguments in Mochizuki's IUT and Kirti Joshi's p-adic Teichmuller constructions. General group-structure claims without this ana

Mochizuki's Key Principle of Inter-Universality requires arbitrary geometric base-points for tempered fundamental groups, which only algebraically closed perfectoid fields supply.

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 →Number theory Inter-universal Teichmüller theory Algebraic geometryimportance · minorImportance 0.30, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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