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For a local complete intersection morphism, we establish fibrewise denseness in the n-dimensional irreducible components of the compactification Nisnevich locally.

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Abstract We prove that, under mild hypothesis, every normal algebraic space that satisfies the $1$-resolution property is quasi-affine. More generally, we show that for algebraic stacks satisfying similar hypotheses, the 1-resolution property guarantees the existence of a finite flat cover by a quasi-affine scheme.