  Let $k$ be a field that is finitely generated over its prime field. In
Grothendieck's anabelian letter to Faltings, he conjectured that sending a
$k$-scheme to its \'{e}tale topos defines a fully faithful functor from the
localization of the category of finite type $k$-schemes at the universal
homeomorphisms to a category of topoi. We prove Grothendieck's conjecture for
infinite fields of arbitrary characteristic. In characteristic $0$, this shows
that seminormal finite type $k$-schemes can be reconstructed from their
\'{e}tale topoi, generalizing work of Voevodsky. In positive characteristic,
this shows that perfections of finite type $k$-schemes can be reconstructed
from their \'{e}tale topoi.
