Key Words: Anabelian geometry, function fields, Riemann-Zariski space, (generalized) [quasi] prime divisors, decomposition graphs, Hilbert decomposition theory, pro- Galois theory, algebraic/étale fundamental group, (split) [semi-stable] families of curves, alteration/modification theory, -adic/Prontrjagin duality.
2000 Mathematics Subject Classification: Primary: 12E, 12F, 12G, 12J;
Secondary: 12E30, 12F10, 12G99.
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