# Morphisms and cohomology comparison for Henselian schemes

Abstract: The geometric counterpart of a Henselian pair is the notion of Henselian schemes, which can serve as an algebraic'' substitute for formal schemes in applications such as deformation theory. In this talk I will discuss Henselian schemes and quasi-coherence, and will also develop the theory of smooth and étale morphisms of Henselian schemes. Finally, I prove a GAGA-style cohomology comparison result for Henselian schemes in positive characteristic, and discuss algebraizability of coherent sheaves on the Henselization of a proper scheme.