I see everywhere says the following: Let $B$ be an indefinite quaternion algebra over $\mathbb{Q}$ of discriminant $D$, $\mathcal{O}_B$ be a maximal order, $N$ be an positive integer coprime to $D$. Consider the moduli problem:

For any scheme $S$, let $F(S)=\{(A,\iota,\alpha)\}$, where $A$ is an abelian surface over $S$, $\iota:\mathcal{O}\to End_S(A)$, and $\alpha$ is a level $N$ structure on $A$. Then $F$ is represented by a Deligne-Mumford stack.

However, I cannot find a reference which actually proves that $F$ satisfies those axioms that one uses to a stack.

Thanks a lot.

I see everywhere the following:

Let $B$ be an indefinite quaternion algebra over $\mathbb{Q}$ of discriminant $D$, $\mathcal{O}_B$ be a maximal order, $N$ be an positive integer coprime to $D$. 

Consider the moduli problem: for any scheme $S$, let $F(S)=\{(A,\iota,\alpha)\}$, where $A$ is an abelian surface over $S$, $\iota:\mathcal{O}\to End_S(A)$, and $\alpha$ is a level $N$ structure on $A$. Then $F$ is represented by a Deligne-Mumford stack.

However, I cannot find a reference which actually proves that $F$ satisfies those axioms that one uses to a stack.

Thanks a lot.

I see everywhere says the following: Let $B$ be an indefinite quaternion algebra over $\mathbb{Q}$ of discrimiant $D$, $\mathcal{O}_B$ be a maximal order, $N$ be an positive integer coprime to $D$. Consider the moduli probelem:

For any scheme $S$, let $F(S)=\{(A,\iota,\alpha)\}$, where $A$ is an ableian surface over $S$, $\iota:\mathcal{O}\to End_S(A)$, and $\alpha$ is a level $N$ structure on $A$. Then $F$ is represented by a Delogne-Mumford stack.

However, I cannot find a reference which actually proves that $F$ satisfies those axioms that one uses to a stack.

Thanks a lot.

I see everywhere says the following: Let $B$ be an indefinite quaternion algebra over $\mathbb{Q}$ of discriminant $D$, $\mathcal{O}_B$ be a maximal order, $N$ be an positive integer coprime to $D$. Consider the moduli problem:

For any scheme $S$, let $F(S)=\{(A,\iota,\alpha)\}$, where $A$ is an abelian surface over $S$, $\iota:\mathcal{O}\to End_S(A)$, and $\alpha$ is a level $N$ structure on $A$. Then $F$ is represented by a Deligne-Mumford stack.

However, I cannot find a reference which actually proves that $F$ satisfies those axioms that one uses to a stack.

Thanks a lot.

I see everywhere says the following: Let $B$ be an indefinite quaternion algebra over $\mathbb{Q}$ of discrimiant $D$, $\mathcal{O}_B$ be a maximal order, $N$ be an positive integer coprime to $D$. Consider the moduli probelem:

For any scheme $S$, let $F(S)=\{(A,\iota,\alpha)\}$, where $A$ is an ableian surface over $S$, $\iota:\mathcal{O}\to End_S(A)$, and $\alpha$ is a level $N$ structure on $A$. Then $F$ is represented by a Delogne-Mumford stack.

However, I cannot find a reference which actually proves that $F$ satisfied those axioms that one uses to a stack.

Thanks a lot.

I see everywhere says the following: Let $B$ be an indefinite quaternion algebra over $\mathbb{Q}$ of discrimiant $D$, $\mathcal{O}_B$ be a maximal order, $N$ be an positive integer coprime to $D$. Consider the moduli probelem:

For any scheme $S$, let $F(S)=\{(A,\iota,\alpha)\}$, where $A$ is an ableian surface over $S$, $\iota:\mathcal{O}\to End_S(A)$, and $\alpha$ is a level $N$ structure on $A$. Then $F$ is represented by a Delogne-Mumford stack.

However, I cannot find a reference which actually proves that $F$ satisfies those axioms that one uses to a stack.

Thanks a lot.