20/04/27 21:23:56 C+LmQa7Q.net
>>493
>p-adicの話にrational numbersが含まれるって？冗談だろ？
お答えします。確かに、Joshi氏論文で characteristic zeroが出てくるのは
P61 Perfectoid algebraic geometry as an example of anabelomorphy のところ（下記引用）
で、”In Section 24, I have stressed the analogy between the theory of perfectoid spaces as developed by [Sch12b] (also see [FF], [SW]) and Mochizuki’s idea of anabelomorphy. ”
のところです
Joshi氏論文 URLﾘﾝｸ(arxiv.org) Kirti Joshi April 24, 2020
表題 On Mochizuki’s idea of Anabelomorphy and its applications
P61
24 Perfectoid algebraic geometry as an example of anabelomorphy 61
Now let me record the following observation which I made in the course of writing [Jos19a] and [Jos19b].
In treatment [DJ] we hope to establish many results of Section 3 of classical anabelian geometry in the perfectoid setting.
Let K be a complete perfectoid field of characteristic zero. Let K♭ be its tilt. Let L be another perfectoid field with L♭ =～ K♭
In Section 24, I have stressed the analogy between the theory of perfectoid spaces as developed by [Sch12b] (also see [FF], [SW]) and Mochizuki’s idea of anabelomorphy.
The proof of the fundamental theorem of Scholze (see [Sch12a]) shows that there exist varieties (in any dimension) over fields of arithmetic interest (i.e. perfectoid fields) which are not isomorphic but which have isomorphic ´etale fundamental groups.
In fact these varieties are even complete intersections.
Importantly in the theory of [Sch12a] and [SW] the fact that there are many untilts (over perfectoid fields of characteristic zero) of a variety over a perfectoid field in characteristic p should be viewed as providing examples of varieties over (non-isomorphic) perfectoid fields of characteristic zero with isomorphic ´etale fundamental group.
Notably one has the following consequence of the remarkable [Wei17, Theorem A] (also see [SW]):
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