現代数学の系譜工学物理雑談古典ガロア理論も読む79

[過去ﾛｸﾞ] 現代数学の系譜工学物理雑談古典ガロア理論も読む79 (1002ﾚｽ)
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53: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [sage] 2019/11/19(火) 13:52:36.20 ID:NP7FWnJl

>>49 関連

Inter-universal geometry と ABC予想 42
https://rio2016.5ch.net/test/read.cgi/math/1572150086/253-
より

https://repository.kulib.kyoto-u.ac.jp/dspace/handle/2433/244782
https://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/244782/1/B76-01.pdf
タイトル:  Mono-anabelian Reconstruction of Number Fields (On the examination and further development of inter-universal Teichmuller theory)
著者:  Hoshi, Yuichiro
発行日:  Aug-2019
出版者:  Research Institute for Mathematical Sciences, Kyoto University
誌名:  数理解析研究所講究録別冊 = RIMS Kokyuroku Bessatsu

Abstract
The Neukirch‐Uchida theorem asserts that every outer isomorphism between the absolute
Galois groups of number fields arises from a uniquely determined isomorphism between the
given number fields. In particular, the isomorphism class of a number field is completely deter‐
mined by the isomorphism class of the absolute Galois group of the number field. On the other
hand, neither the Neukirch‐Uchida theorem nor the proof of this theorem yields an “explicit
reconstruction of the given number field”. In other words, the Neukirch‐Uchida theorem only
yields a bi‐anabelian reconstruction of the given number field. In the present paper, we discuss
a mono‐anabelian reconstruction of the given number field. In particular, we give afunctorial
“group‐theoretic” algorithm for reconstructing, from the absolute Galois group of a number
field, the algebraic closure of the given number field [equipped with its natural Galois action]
that gave rise to the given absolute Galois group.

つづく

http://rio2016.5ch.net/test/read.cgi/math/1573769803/53

54: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [sage] 2019/11/19(火) 13:53:15.26 ID:NP7FWnJl

>>53

つづき

One important step of our reconstruction
algorithm consists of the construction of a global cyclotome [i.e., a cyclotome constructed from
a global Galois group] and a local‐global cyclotomic synchronization isomorphism [i.e., a suit‐
able isomorphism between a global cyclotome and a local cyclotome]. We also verify a certain
compatibility between our reconstruction algorithm and the reconstruction algorithm given by
S. Mochizuki concerning the etale fundamental groups of hyperbolic orbicurves of strictly Be‐
lyi type over number fields. Finally, we discuss acertain global mono‐anabelian log‐Frobenius
compatibility property satisfied by the reconstruction algorithm obtained in the present paper.
Contents
§0. Notations and Conventions
§1. Review of the Local Theory
§2. Reconstruction of the Additive Structure on an NF‐monoid
§3. Local‐global Cyclotomic Synchronization
§4. Reconstruction of the Additive Structure on a GSC‐Galois Pair
§5. Mono‐anabelian Reconstruction of Number Fields
§6. Global Mono‐anabelian {\rm Log}‐Frobenius Compatibility
(引用終り)
以上

http://rio2016.5ch.net/test/read.cgi/math/1573769803/54

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