Florian Pop: On the minimized decomposition theory of valuations, p.331-357

Abstract:

In this note we discuss the behavior of minimized inertia/decomposition groups of valuations, and prove similar results to the ones for tame inertia. The results are technical tools for a host of questions in Bogomolov's birational anabelian program.

Key Words: Anabelian geometry, function fields, Riemann-Zariski space, (generalized) [quasi] prime divisors, decomposition graphs, Hilbert decomposition theory, pro-$\ell$ Galois theory, algebraic/étale fundamental group, (split) [semi-stable] families of curves, alteration/modification theory, $\ell$-adic/Prontrjagin duality.

2000 Mathematics Subject Classification: Primary: 12E, 12F, 12G, 12J;
Secondary: 12E30, 12F10, 12G99.

Download the paper in pdf format here.