[過去ﾛｸﾞ] Inter-universal geometry とABC 予想55 (1002ﾚｽ)
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8: 2024/04/14(日)10:09 ID:scyNFM/R(1/4) AAS
Peter Scholze

I'm more afraid that this is an instance where the cited reference does not match the statement that is claimed. The critical difference between Joshi and Mochizuki is that "Joshi's version of Mochizuki's Corollary 3.12" (=Joshi's Theorem 9.11.1) has a purely local proof and hence cannot have the same content as Mochizuki's Corollary 3.12. However, it may be correct on its own; then the mistake is a mismatch between what Joshi has to compute in Proposition 6.10.7, and what Mochizuki actually computed in IUT IV. But I agree with Sam Hopkins that this discussion is not fruitful. –

外部ﾘﾝｸ:mathoverflow.net

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9: 2024/04/14(日)10:10 ID:scyNFM/R(2/4) AAS
Peter Scholze

To summarize: There is a clear problem with Joshi's proof, as there is a contradiction between Proposition 6.10.7 and the local inequality proved in the proof of Theorem 9.11.1. The mistake could be in Proposition 6.10.7 (and, given that the proof isn't written down, is the first suspicious place) but it might as well be a mistake in the proof of Theorem 9.11.1. In any case, this whole discussion is only about Joshi's proof, not Mochizuki's; I do not think that there is a real error internally in IUT IV.

外部ﾘﾝｸ:mathoverflow.net

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12(3): 2024/04/14(日)13:04 ID:scyNFM/R(3/4) AAS
Peter Scholze

I do not think that there is a real error internally in IUT IV.

real error 　→　〇：真のエラー、×：とりあえず矛盾　

ペーター　ショルツェ
私はIUT-?内に真のエラーがないと考える。

・IUT-?を使って、IUT-?でABC予想の不等式をつくるので、IUT-?にはIUT-?を前提で含んでいる
・従い、IUT-?過程とIUT‐?に至る過程の前提にも、真のエラーがない

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13: 2024/04/14(日)13:05 ID:scyNFM/R(4/4) AAS
IUT勝利

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