Lemma 109.57.1. There exists a sheaf of abelian groups $G$ on $\mathit{Sch}_{\acute{e}tale}$ with the following properties

1. $G(\mathop{\mathrm{Spec}}(k)) = 0$ whenever $k$ is a field,

2. $G$ is limit preserving,

3. if $X \subset X'$ is a thickening, then $G(X) = G(X')$, and

4. $G$ is not zero.

Proof. See discussion above. $\square$

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