Loading [MathJax]/extensions/tex2jax.js

The Stacks project

Lemma 101.19.2. Let $\mathcal{X}$ be an algebraic stack. Let $x \in |\mathcal{X}|$ be a point. Let $P$ be a property of algebraic spaces over fields which is invariant under ground field extensions; for example $P(X/k) = X \to \mathop{\mathrm{Spec}}(k)\text{ is finite}$. The following are equivalent

  1. for some morphism $x : \mathop{\mathrm{Spec}}(k) \to \mathcal{X}$ in the class of $x$ the automorphism group algebraic space $G_ x/k$ has $P$, and

  2. for any morphism $x : \mathop{\mathrm{Spec}}(k) \to \mathcal{X}$ in the class of $x$ the automorphism group algebraic space $G_ x/k$ has $P$.

Proof. Omitted. $\square$


Comments (0)

There are also:

  • 2 comment(s) on Section 101.19: Automorphism groups

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.