Let $X$ be a locally noetherian regular scheme and $Y$ be a closed subscheme of codimension $d > 0$ in every point. Why does it "immédiatement" (Grothendieck, Groupe de Brauer III, §6, p. 133 f.) follow that the local cohomology sheaves with supports $\mathcal{H}^i_Y(X,\mathbf{G}_m)$ vanish for $0 \leq i \leq 2$ (if $d \neq 1$ for $i=1$)?

(For $i \neq 0$, it would be clear to me if there were no supports: The stalks are zero since the Picard group of a local ring and the Brauer group of a strictly henselian local ring vanish.)