20/10/25 09:24:26.06 eIdDsFH8.net
>>596
つづき
Finally, in passing, we note that this discussion applies, albeit in perhaps a somewhat
trivial way, to the isomorphism of Galois groups ΨηX : GK～→ GK induced by the
Frobenius morphism ΦηX in Example 2.6.1, (i): That is to say, from the point of view
of classical ring theory, this isomorphism of Galois groups is easily seen to coincide with
the identity automorphism of GK. On the other hand, if one takes the point of view
that elements of various subquotients of GK are equipped with labels that arise from
the isomorphisms ρ or κ of Example 2.6.1, (ii), (iii), i.e., from the reciprocity map of
class field theory or Kummer theory, then one must regard such labelling apparatuses
as being incompatible with the Frobenius morphism ΦηX . Thus, from this point
of view, the isomorphism ΦηX must be regarded as a “mysterious, indeterminate
isomorphism” [cf. the discussion of §2.7, (iii)].
(引用終り)
以上