For an algebraic stack [math] \mathfrak{X} \to {S_{Et}} [/math]

Ok so I have been playing with the definition and this seems to imply that schemes over stacks with representable diagonal can glue to give more schemes.

Am I on the right track? Someone on /sci/ must know this.

/sci/ is useless

>>8492197
most /sci/-goers aren't math grad students

try the math stack exchange

>>8491529

Why do you need to know? Learning schemes for its own sake is just going to be an exercise in syntax and substitution rules and you won't be able to visualize any of it.

>>8492298
I am not learning schemes. I am learning about stacks.

One of the conditions for an algebraic stack to be Deligne-Mumford is for its diagonal morphism to be representable. This means for any two schemes over the stack, their fibered product over the stack is representable by a scheme in the usual functor sense.

I want to know what properties this condition is trying to capture. I think it telling us something about gluing but am not sure.

>>8492197
OP must be useless if this is the first place he/she comes for help learning about stacks

>>8492217

Whats the problem with that? Is being a math grad a must be to join /sci/? Im studying masters in mechanical engineering so im not supose to be here? Tell me more about that, annon

>>8492455
no the problem is that he's unlikely to get a good answer to his question here

>>8492455
You are insecure anon.

>>8492455
No , you are not supose

>>8491347
Big N, is that you?

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The condition is equivalent to the following local condition: if we have $\xi\in \mathfrak{X}(U)$ and $\nu\in \mathfrak{X}(V)$, for $U, V$ affine schemes. This is equivalent to the data of maps $h_U\to \mathfrak{X}$, and $h_V\to \mathfrak{X}$, where $h_U$ is the stacks that are represented by $U$. Then the condition that the diagonal be representable is just that $h_U\times_{\mathfrak{X}}h_V$ is represented by a scheme.