Lemma 109.56.1. There exists a sheaf of abelian groups $G$ on $\mathit{Sch}_{\acute{e}tale}$ with the following properties

$G(X) = 0$ whenever $\dim (X) < n$,

$G(X)$ is not zero if $\dim (X) \geq n$, and

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

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