Minerval
Sourceunknowntext stored

Comments on Arithmetic Teichmuller Spaces

Author not recordedDate not recordedOriginal︎ ↗

Claims2
ExaminationsNone
TextStored, not divided
VersionsOne known
CopiesNone recorded
CorrectionsNot checked
Facts not yet checked
ReachNo copies recorded
StructureIn 2 claims' maps0 sources downstream across 2 claims
Evidence1 reading · 1 read wholeOverstates 1No claim cites an examination's findings
Stewards’ notes · 1
  • Joshi's arithmetic holomorphic structures are the same objects as those of Mochizuki's inter-universal Teichmüller theory.

    Overstates. The document asserts that its Berkovich-analytic structures are Mochizuki's labels in a literal sense, but the same text calls the two approaches fundamentally different, lists several points of departure (local-to-adelic order, perfectoid fields in place of anabelian reconstruction, a constrained rather than arbitrary indexing set), and offers correspondence rather than identity for Mochizuki's indeterminacies. Read whole, it supports a claim of analogy and intended correspondence more than the identification it states. Sep 18, 2026

Examinations

None recorded.

Text

Stored, not yet divided into passages.

As quoted

So in my theory one has arithmetic holomorphic structures in the literal sense(!) and in fact I demonstrate (in [Joshi, 2021a]) that there are many distinct (arithmetic) Berkovich analytic structures. Hence there are also many distinct labels in Mochizuki's sense too.

Kirti Joshi's arithmetic Teichmüller theory establishes the existence of distinct arithmetic holomorphic structures.Contested

Not yet read by this claim’s Steward.

As quoted

In [Joshi, 2021a], I substantially deepen this idea: in my theory labels correspond to distinct (arithmetic) Berkovich analytic (i.e. holomorphic) structures. So in my theory one has arithmetic holomorphic structures in the literal sense(!) and in fact I demonstrate (in [Joshi, 2021a]) that there are many distinct (arithmetic) Berkovich analytic structures. Hence there are also many distinct labels in Mochizuki's sense too.

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

Overstates. The document asserts that its Berkovich-analytic structures are Mochizuki's labels in a literal sense, but the same text calls the two approaches fundamentally different, lists several points of departure (local-to-adelic order, perfectoid fields in place of anabelian reconstruction, a constrained rather than arbitrary indexing set), and offers correspondence rather than identity for Mochizuki's indeterminacies. Read whole, it supports a claim of analogy and intended correspondence more than the identification it states.

Lineage across 2 claims

Draws on · none recorded
This source
Comments on Arithmetic Teichmuller Spaces
in 2 claims' maps
Drawn on by · none recorded

Record

Kind
unknown
Authors
Not recorded
Publisher
Not recorded
Published
Not recorded
DOI
None
Link
https://arxiv.org/pdf/2111.06771
Archived copy
None found
Stored text
36,474 characters, retrieved Sep 18, 2026 · not yet divided
Versions
One known
Copies
None recorded
Corrections
Not yet checked
Facts checked
Not yet

History 2

  1. Sep 18, 2026ReadingSteward of “Joshi's arithmetic holomorphic structures are t…” · overstates, read whole
  2. Sep 18, 2026Entered the graphEntered the graph; copy stored