fpqc morphism

In algebraic geometry, there are two slightly different definitions of an fpqc morphism, both variations of faithfully flat morphisms.

Sometimes an fpqc morphism means one that is faithfully flat and quasi-compact.

This is where the abbreviation fpqc comes from: fpqc stands for the French phrase "fidèlement plat et quasi-compact", meaning "faithfully flat and quasi-compact".

However it is more common to define an fpqc morphism

of schemes to be a faithfully flat morphism that satisfies the following equivalent conditions: Examples: An open faithfully flat morphism is fpqc.