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https://mathoverflow.net/a/435112

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Joshi's arithmetic holomorphic structures are the same objects as those of Mochizuki's inter-universal Teichmüller theory.
Supports. Scholze gives a specific argument: in Joshi's Theorem 4.8 the curve and its tempered fundamental group stay fixed and only the embedding of the base field into an untilt varies, so the added data is not something the fundamental group could see, and calling it an arithmetic holomorphic structure is a relabeling. The argument is brief but self-contained and addresses the definition rather than the reputation of the work. Sep 18, 2026

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$\begingroup$ For some categories $C$ and $D$, there's a functor from $C$ to $D$, and we claim (and prove! -- by citing an old paper of Mochizuki) that this functor is fully faithful. Joshi defines a category $C'$ with a non-fully-faithful forgetful functor $C'\to C$ by endowing objects of $C$ with some extra data, and then notes that $C'\to C\to D$ is not fully faithful. Joshi makes the linguistic trick of calling the extra data he puts on objects of $C$ an "arithmetic holomorphic structure", but this is just linguistics... $\endgroup$

Joshi's arithmetic holomorphic structures are the same objects as those of Mochizuki's inter-universal Teichmüller theory.ContradicteddeniesReading · this claim’s Steward

Supports. Scholze gives a specific argument: in Joshi's Theorem 4.8 the curve and its tempered fundamental group stay fixed and only the embedding of the base field into an untilt varies, so the added data is not something the fundamental group could see, and calling it an arithmetic holomorphic structure is a relabeling. The argument is brief but self-contained and addresses the definition rather than the reputation of the work.

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Untilts of fundamental groups: construction of labeled isomorphs of fundamental groups -- Arithmetic Holomorphic StructuresunknownOct 20, 20221 claimResponds to it faithfully, on 1 claim.

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Link: https://mathoverflow.net/a/435112
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Stored text: 19,628 characters, retrieved Sep 18, 2026 · 219 sections, 174 passages
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Versions: One known
Copies: None recorded
Corrections: None recorded
Facts checked: Nov 9, 2026

History 4

Nov 9, 2026DividedSegmenter · Divided into 393 parts by its own structure
Nov 9, 2026FactsFacts fetcher · Facts looked up
Sep 18, 2026ReadingSteward of “Joshi's arithmetic holomorphic structures are t…” · supports, read whole
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