  An $F$-nilpotent local ring is a local ring $(R, \mathfrak{m})$ of prime
characteristic defined by the nilpotence of the Frobenius action on its local
cohomology modules $H^i_{\mathfrak{m}}(R)$. A singularity in characteristic
zero is said to be of $F$-nilpotent type if its modulo $p$ reduction is
$F$-nilpotent for almost all $p$. In this paper, we give a Hodge-theoretic
interpretation of three-dimensional normal isolated singularities of
$F$-nilpotent type. In the graded case, this yields a characterization of these
singularities in terms of divisor class groups and Brauer groups.
