Fpqc morphism

Okay, so let's imagine you have two houses. Both houses look similar from the outside, but when you go inside, they have different rooms and decorations.

Now, let's say you want to connect these two houses by building a road between them. But you don't want the road to just go straight from one house to the other, because there might be obstacles like trees or rocks in the way. So instead, you decide to make a lot of little paths that weave around the obstacles, kind of like a maze.

This is kind of what a fpqc morphism is like. It's a way to connect two mathematical objects, but instead of just drawing a straight line between them, you have to weave around obstacles.

The "fpqc" part stands for "faithfully flat and quasi-compact." This means the path you're building has to be flat (like a sheet of paper) and compact (like a small box), but it also has to keep all the important information about the houses intact.

So putting it all together: a fpqc morphism is like building a maze-like path between two mathematical objects, while making sure all the important information stays the same.