>>798
>§ 1.4 Final Conclusion
>This report also applies to, and invalidates, the discussions of Mochizuki’s work on Peter Woit’s Blog, especially but not limited to [Scholze et al., April 2020],

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(参考)
Columbia Math Department
https://www.math.columbia.edu/~woit/szpirostillaconjecture.pdf
2020/04/19 — This document is a lightly edited version of the mathematically substantive comments posted from April 6 - April 19, 2020 at this blog ...
(引用開始)
kirti joshi April 8, 2020 at 10:15 am
Dear Professor Woit,
This is to clarify the claims made about my paper in the context of your abc blog-post. First of all let me say that my paper (referred to by Scholze in his comments) is not a survey of Mochizukis work (though it may initially appear so because I state a number of standard results without proofs) and contains a number of new and original results (Scholze agrees with me on this). I start with one of Mochizukis ideas and I build upon it in my paper. This is the paper which is cited in Scholzes comments and which can be found on the arxiv (though the update is not yet ready). In our correspondence Scholze has agreed (mostly) with all the changes in the new version and we (i.e. Scholze, Hoshi and myself) continue to correspond to resolve any persisting issues (of which there are very few).
略
(6) In my paper I have also pointed out the analogy between Scholzes work (deeply extending earlier work of Fontaine) and Mochizukis idea (see the section on perfectoid spaces in my paper) and in our personal correspondence Scholze has said that he sees no issues with my claims in that section (modulo minor corrections). In particular I point out in that section that Scholzes work is founded on a similar idea of changing perfectoid fields, perfectoid varieties (instead of p-adic elds and curves over p-adic fields) while keeping the absolute Galois group (of the perfectoid field) xed (resp. etale fundamental group fixed). In the parlance of perfectoid geometry this corresponds to moving from one untilt to another untilt see my paper for details (or Scholzes paper). Deepening of this analogy (as Taylor Dupuy and I hope to do in an ongoing project) should provide further insights into this difficult topic.

(7) The following way of remembering Mochizukis idea may be useful: A p-adic eld wiggles and moves around in the isomorphism class of its absolute Galois group. This wiggling is a (new) degree of freedom in number theory and in algebraic geometry. (This is illustrated in my paper with explicit examples and also see Mochizukis paper and Hoshis work and other members of the Kyoto school).