Inter-universal geometry と ABC予想 (応援スレ) 44at MATH
Inter-universal geometry と ABC予想 (応援スレ) 44 - 暇つぶし2ch427:rgen Neukirch (1969) showed that two algebraic number fields with the same absolute Galois group are isomorphic, and Koji Uchida (1976) strengthened this by proving Neukirch's conjecture that automorphisms of the algebraic number field correspond to outer automorphisms of its absolute Galois group. Florian Pop (1990, 1994) extended the result to infinite fields that are finitely generated over prime fields. The Neukirch?Uchida theorem is one of the foundational results of anabelian geometry, whose main theme is to reduce properties of geometric objects to properties of their fundamental groups, provided these fundamental groups are sufficiently non-abelian. References https://www.jstor.org/stable/2946630?origin=crossref&seq=1 Pop, Florian (1994), "On Grothendieck's conjecture of birational anabelian geometry" Annals of Mathematics




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