>>32
つづき

Mochizuki considers infinitely many distinct isomorphic copies of π1(X)’s, but could not tell us what goes wrong if we simply identify all of them with one another, and with π1(X)
for some fixed Xo
? there is no diagram that commutes in his situation but does not commute under this further identification. (In my manuscript with Stix, we simply went through Mochizuki’s argument with this further identification, pinpointing what goes wrong. If this further identification causes problems, just tell us which diagram it is whose commutativity is rescued by not explicitly identifying π1(X)’s.)

However, what I really want to do with this comment is to point out that there seems to be significant confusion over just the above point on X’s vs π1(X)’s.
Recently, arXiv:2003.01890v1 appeared, in which the author (Kirti Joshi) gives some survey on results related to Mochizuki’s work. In the introduction, on page 7, he explicitly claims that one could find non-isomorphic X’s giving rise to the same π1(X), and even more, in Remark 2.1 on page 14 he explains that my reading of the situation is a common misunderstanding. Even more, in Corollary 21.2 on page 47, he states something “well-known to everyone at RIMS” giving an explicit example of this phenomenon of non-isomorphic X’s giving rise to the same π1(X).

つづく