Torsor (algebraic geometry)

Okay, so you know how sometimes you have two things that seem different but they're actually the same? Like how a bike and a scooter both have wheels and handlebars, even though they look different. In algebraic geometry, we call this a "torsor".

A torsor is kind of like a playground slide. It's a thing you can play on that has a certain shape and structure, but it doesn't really matter where that slide is located. You can pick it up and move it around to different places, and it's still the same slide.

In algebraic geometry, a torsor is a group of things that all have the same shape and structure, but they might be located in different places. And just like with the slide, it doesn't really matter where they are. The important thing is that they all have the same structure and you can do the same things with them.

So let's say you have a group of puppies, and all the puppies have the same collar. The collar is the "structure" that they have in common. But the puppies might be located in different places – some might be at home, some might be at the park, some might be at the pet store. Even though they're in different places, they all have the same collar and you can do the same things with them.

That's kind of what a torsor is in algebraic geometry. It's a group of things that have the same structure, but they might be located in different places. And just like with the puppies, you can do the same things with them no matter where they are.