The Stacks project

Lemma 109.72.1. Let $k$ be an algebraically closed field which is not the closure of a finite field. Let $A$ be an abelian variety over $k$. Let $\mathcal{X} = [\mathop{\mathrm{Spec}}(k)/A]$. There exists an inverse system of $k$-algebras $R_ n$ with surjective transition maps whose kernels are locally nilpotent and a system $(\xi _ n)$ of $\mathcal{X}$ lying over the system $(\mathop{\mathrm{Spec}}(R_ n))$ such that this system is not effective in the sense of Artin's Axioms, Remark 97.20.2.

Proof. See discussion above. $\square$

Comments (0)

Post a comment

Your email address will not be published.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.

In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 0CXX. Beware of the difference between the letter 'O' and the digit '0'.