21/08/26 07:34:11.51 V/6zn5VS.net
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つづき
Anabelian geometry is a sort of utmost non-abelian and non-linear theory, working with full topological
groups such as the absolute Galois groups and fundamental groups of hyperbolic curves (smooth projective geometrically connected curve whose Euler characteristic is negative). Rigidity of certain Galois and fundamental
groups is a key feature of anabelian geometry.
Tamagawa’s theorem states that for two non-proper hyperbolic curves C1,C2 over a finitely generated field
k over Q, the natural morphism from k-isomorphisms of k-schemes C1 to C2 to continuous Gk-isomorphisms
of their etale fundamental groups modulo inner automorphisms of the etale fundamental group of C2 ×k k alg
is bijective, [60]. One of Mochizuki’s theorem extends this property to all hyperbolic curves, [45]. Another
much stronger theorem of Mochizuki states that the natural morphism from dominant k-morphisms of hyperbolic curves C1,C2 over a subfield k of a field finitely generated over p-adic numbers to open continuous Gkhomomorphisms of their etale fundamental groups, considered up to composition with an inner automorphism of the etale fundamental group of C2 ×k k alg, is bijective, [46], [47].
つづく