Publication:
A Note On Cohomology Over Non Algebraically Closed Fields

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http://journals.cambridge.org/download.php?file=%2FBAZ%2FBAZ60_01%2FS0004972700033335a.pdf&code=d528a7711
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Publication Date
1999
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Australian Mathematics
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Abstract
We characterise algebraically closed fields as those for which the first cohomology group tf^fc^On) of the sheaf On of regular functions over kn vanishes for all positive intergers n.
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Geometria algebraica
Unesco subjects
1201.01 Geometría Algebraica
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R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics 52 (Springer-Verlag,Berlin, Heidelberg, New York, 1977). J.P. Serre,'Faisceaux algebriques coherents', Ann. of Math. Stud. 61 (1955), 197-258. 72 J.M. A. Tognoli, 'Some basic facts in algebraic geometry on a non algebraically closed field', Ann. Scuola Normal Sup. Pisa Cl. Sci. 3 (1976), 341-359.
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https://hdl.handle.net/20.500.14352/57266
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