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$\mathbb{Z}/p$ metabelian birational 
$p$-adic section conjecture for varieties
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.
