  In this note, we discuss a streamlined proof of a result due to Milne
computing special values of zeta functions for smooth proper schemes over a
finite field $\mathbb{F}_q$. The proof will give a natural interpretation of
the correction factor in terms of invariants constructed from prismatic
cohomology, studied by Morin. We then discuss the modifications needed when
passing from the smooth case to an arbitrary qcqs scheme $X$ of finite type
over $\mathbb{F}_q$, at least assuming a strong form of resolution of
singularities.
