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A Note On Cohomology Over Non Algebraically Closed Fields

Gamboa Mutuberria, José Manuel (1999) A Note On Cohomology Over Non Algebraically Closed Fields. Bulletin Of The Australian Mathematical Society, 60 (1). pp. 67-72. ISSN 0004-9727

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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.

Item Type:Article
Uncontrolled Keywords:Sheaf Of Regular Functions; First Cohomology Group; Algebraically Closed Fields
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:15328
References:

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.

Deposited On:23 May 2012 08:41
Last Modified:06 Feb 2014 10:22

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