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.
$\square$

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