Definition
If \(\mathcal X\) is an algebraic stack and \(x:\Spec k \to \mathcal X\) is a field valued point then the stabilizer of \(x\) (or automorphism group of \(x\)) is the algebraic group \(G_x = \Aut_{\mathcal X(k)}(x)\).
Definition
If \(\mathcal X\) is an algebraic stack and \(x:\Spec k \to \mathcal X\) is a field valued point then the stabilizer of \(x\) (or automorphism group of \(x\)) is the algebraic group \(G_x = \Aut_{\mathcal X(k)}(x)\).