>>944 追加

Tate twist Z＾(1)、
Tate module Z＾(1) とも書かれている
Jakob Stixの論文だが

https://projecteuclid.org/proceedings/advanced-studies-in-pure-mathematics/GaloisTeichm%C3%BCller-Theory-and-Arithmetic-Geometry/Chapter/On-cuspidal-sections-of-algebraic-fundamental-groups/10.2969/aspm/06310519
Advanced Studies in Pure Mathematics 63, 2012
Galois-Teichmiiller Theory and Arithmetic Geometry pp. 519-563

On cuspidal sections of algebraic fundamental groups Jakob Stix
（Editor(s) Hiroaki Nakamura, Florian Pop, Leila Schneps, Akio Tamagawa）

P524
§2. Fields with nontrivial Kummer theory
Definition 2. The pro-N completion of an abelian group A is
A＾＝lim ←N A/nA

Tate module Z＾(1) = lim ←n μn.

P540
§7. Orientation and degree
As it matters here, we stress that the Tate twist Z＾(1) has an anabelian
definition as the geometric fundamental group πr1 (G?m) of Gm
with the Galk-action induced from π1(Gm/k).

P543
§8. Anabelian theory of units

Before we start the proof we recall that we identify π1 (G?) = Z＾(1) and that the Tate-module Z＾(1) is defined as lim←n μln.
We therefore write composition in Z＾(1) multiplicatively.
Additive notation would suggest having chosen an isomorphism Z＾(1) 〜＝ Z＾ of the underlying pro-finite groups, i.e., having chosen a compatible system of roots of unity, a choice that we avoid to make.
(引用終り)
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