J. M. Gamboa
Abstract
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We characterise algebraically closed fields as those for which the first cohomology group H1(kn, On) of the sheaf On of regular functions over kn vanishes for all positive intergers n.
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We characterise algebraically closed fields as those for which the first cohomology group H1(kn, On) of the sheaf On of regular functions over kn vanishes for all positive intergers n.
Key concepts: Mathematics, Algebraically closed field, Cohomology, Pure mathematics, Sheaf, Sheaf cohomology, Étale cohomology, Group cohomology