# Cohomology groups on small fppf site and small etale site are not the same

Let $$F$$ be a quasi-coherent sheaf on a scheme $$X$$. Is there an example where cohomology groups of $$F$$ on small fppf site of $$X$$ and small etale site of $$X$$ are not isomorphic?

• If the scheme is a "usual" scheme (quasi-compact, quasi-separated, etc.), then fppf cohomology, etale cohomology, and Zariski cohomology agree for all quasi-coherent sheaves. – Jason Starr Dec 24 '18 at 17:42