Let X be a quasi-compact and quasi-separated algebraic space such that for every quasi-coherent OX-module F we have H1(X, F) = 0. Then X is an affine scheme. See Tag 07V6.
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Algebraic stacks and open source algebraic geometry
Let X be a quasi-compact and quasi-separated algebraic space such that for every quasi-coherent OX-module F we have H1(X, F) = 0. Then X is an affine scheme. See Tag 07V6.