trailJoshi's arithmetic holomorphic structures are the same objects as those of Mochizuki's inter-universal Teichmüller theory.
Kirti Joshi's arithmetic Teichmüller theory establishes the existence of distinct arithmetic holomorphic structures.
Joshi's precisification argument· for
Mochizuki's IUT papers give no definition of arithmetic holomorphic structure precise enough to prove that two such structures differ.
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Mochizuki's Key Principle of Inter-Universality requires arbitrary geometric base-points for tempered fundamental groups, which only algebraically closed perfectoid fields supply.
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Joshi's arithmetic Teichmüller theory yields a valid proof of Mochizuki's Corollary 3.12.
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Different notions under one name· against
In IUT, "distinct arithmetic holomorphic structures" means ring structures related by a non-ring-theoretic link, not non-isomorphic structures.
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The untilt data that defines Joshi's arithmetic holomorphic structures plays no role in the constructions of Mochizuki's IUT papers.
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Joshi's arithmetic holomorphic structures are the same objects as those of Mochizuki's inter-universal Teichmüller theory.
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1depended on by
this rests on ↓
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