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A note on cohomology over non algebraically closed fields

Published online by Cambridge University Press:  17 April 2009

J.M. Gamboa
J.M. Gamboa
Affiliation:
Facultad de MatemáticasUniversidad Complutense de Madrid28040 MadridEspaña e-mail: jmgamboa@eucmax.sim.ucm.es
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 60 , Issue 1 , August 1999 , pp. 67 - 72
Copyright
Copyright © Australian Mathematical Society 1999

References

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[3]Tognoli, A., ‘Some basic facts in algebraic geometry on a non algebraically closed field’, Ann. Scuola Normal Sup. Pisa Cl. Sci. 3 (1976), 341–359.Google Scholar