  The global analogue of a Henselian local ring is a Henselian pair-a ring R
and an ideal I which satisfy a condition resembling Hensel's lemma regarding
lifting coprime factorizations of monic polynomials over R/I to factorizations
over R. The geometric counterpart is the notion of a Henselian scheme, which
can serve as a substitute for formal schemes in applications such as
deformation theory. In this paper we prove a GAGA-style cohomology comparison
result for Henselian schemes in positive characteristic, making use of a
"Henselian \'etale" topology defined in previous work in order to leverage
exactness of finite pushforward for abelian sheaves in the \'etale topology of
schemes. We will also discuss algebraizability of coherent sheaves on the
Henselization of a proper scheme, proving (without a positive characteristic
restriction) algebraizability for coherent subsheaves. We can then deduce a
Henselian version of Chow's theorem on algebraization and the algebraizability
of maps between Henselizations of proper schemes.
