Isomorphisms of fundamental groups of elementary anabelian varieties over sub-p-adic fields correspond bijectively to isomorphisms of the varieties, verifying Grothendieck's conjectures.
Mochizuki,The local pro-p anabelian geometry of curves, English, Invent
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Elementary anabelian varieties are anabelian
Isomorphisms of fundamental groups of elementary anabelian varieties over sub-p-adic fields correspond bijectively to isomorphisms of the varieties, verifying Grothendieck's conjectures.