  We classify Enriques surfaces with smooth K3 cover and finite automorphism
group in arbitrary positive characteristic. The classification is the same as
over the complex numbers except that some types are missing in small
characteristics. Moreover, we give a complete description of the moduli of
these surfaces. Finally, we realize all types of Enriques surfaces with finite
automorphism group over the prime fields $\mathbb{F}_p$ and $\mathbb{Q}$
whenever they exist.

Algebraic Geometry;Number Theory