See Alper Definition 3.2.10 and Exercise 3.2.15.
Definition
Let \(\mathcal X\) be an algebraic stack. The inertia stack of \(\mathcal X\) is the fiber product
[diagram failed to compile]
latex failed:
e named `tikz@f@1-2-1' is known.
See the pgf package documentation for explanation.
Type H <return> for immediate help
...
l.5 I think the culprit is a tikzcd arrow in cell 1-1.
\errmessage ...currentrow -\tikzcd@currentcolumn }
l.7 \end{tikzcd}
! Package pgf Error: No shape named `tikz@f@1-2-1' is known.
See th
In the relative setting \(\mathcal X\to \mathcal Y\), it is the fiber product in the diagram
[diagram failed to compile]
latex failed:
e named `tikz@f@1-2-1' is known.
See the pgf package documentation for explanation.
Type H <return> for immediate help
...
l.5 I think the culprit is a tikzcd arrow in cell 1-1.
\errmessage ...currentrow -\tikzcd@currentcolumn }
l.7 \end{tikzcd}
! Package pgf Error: No shape named `tikz@f@1-2-1' is known.
See th
It is equaivalent to the category of pairs \((x,\alpha)\) where \(x\in \mathcal X(S)\) is an object over \(S\) and \(\alpha \in \Aut_{\mathcal X(S)}(x)\) is in the stabilizer of \(x\). The fiber of \(I_{\mathcal X}\to \mathcal X\) over a field valued point \(x\in \mathcal X(k)\) is precisely the stabilizer group \(G_x\) of \(x\).