Abstract
We generalize the $\mathbb{Z}/p$metabelian birational $p$-adic section conjecture for curves, as introduced and proved in Pop [On the birational$p$-adic section conjecture, Compos. Math. 146 (2010), 621–637], to all complete smooth varieties, provided $p>2$. The condition $p>2$ seems to be of technical nature only, and might be removable.
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