Lemma 59.73.14. Let X be a quasi-compact and quasi-separated scheme. Let \eta \in X be a generic point of an irreducible component of X.
Let \mathcal{F} be a torsion abelian sheaf on X_{\acute{e}tale} whose stalk \mathcal{F}_{\overline{\eta }} is zero. Then \mathcal{F} = \mathop{\mathrm{colim}}\nolimits \mathcal{F}_ i is a filtered colimit of constructible abelian sheaves \mathcal{F}_ i such that for each i the support of \mathcal{F}_ i is contained in a closed subscheme not containing \eta .
Let \Lambda be a Noetherian ring and \mathcal{F} a sheaf of \Lambda -modules on X_{\acute{e}tale} whose stalk \mathcal{F}_{\overline{\eta }} is zero. Then \mathcal{F} = \mathop{\mathrm{colim}}\nolimits \mathcal{F}_ i is a filtered colimit of constructible sheaves of \Lambda -modules \mathcal{F}_ i such that for each i the support of \mathcal{F}_ i is contained in a closed subscheme not containing \eta .
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