Moduli stack of formal group laws
Okay kiddo, let's talk about moduli stacks of formal group laws, or FG moduli stacks for short.
Do you remember what a formal group law is? It's a special way of adding things together, like numbers or coordinates, but it works for anything that can be added. And just like numbers, formal group laws can have different properties, like being commutative or associative.
Now, imagine you have a bunch of formal group laws, all with different properties. And let's say you want to study all of them at once, sort of like putting them all together in a big group. That's where the moduli stack comes in!
A moduli stack basically means a collection of related objects, and in this case, we're collecting all the FGs that we care about. But we need a way to organize them so they don't get too messy. So instead of just stacking them all up like a tower, we arrange them on a graph, which we call the moduli stack.
On the moduli stack, we put the formal group laws based on their properties. FGs with similar properties are next to each other on the graph, and ones with different properties are farther apart. That way, it's easy to see how the different FGs relate to each other and which ones have common features.
Now, why do we care about FG moduli stacks? Well, they're really useful in math, especially in algebraic geometry and number theory. They help us study FGs in a more efficient way, by looking at the properties of the whole group instead of just one FG at a time.
And who knows, maybe one day when you're studying math, you'll get to use FG moduli stacks too!
Do you remember what a formal group law is? It's a special way of adding things together, like numbers or coordinates, but it works for anything that can be added. And just like numbers, formal group laws can have different properties, like being commutative or associative.
Now, imagine you have a bunch of formal group laws, all with different properties. And let's say you want to study all of them at once, sort of like putting them all together in a big group. That's where the moduli stack comes in!
A moduli stack basically means a collection of related objects, and in this case, we're collecting all the FGs that we care about. But we need a way to organize them so they don't get too messy. So instead of just stacking them all up like a tower, we arrange them on a graph, which we call the moduli stack.
On the moduli stack, we put the formal group laws based on their properties. FGs with similar properties are next to each other on the graph, and ones with different properties are farther apart. That way, it's easy to see how the different FGs relate to each other and which ones have common features.
Now, why do we care about FG moduli stacks? Well, they're really useful in math, especially in algebraic geometry and number theory. They help us study FGs in a more efficient way, by looking at the properties of the whole group instead of just one FG at a time.
And who knows, maybe one day when you're studying math, you'll get to use FG moduli stacks too!