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On an analog of Serre’s conjectures, Galois cohomology and defining equation of unipotent algebraic groups
Nguyêñ Quôć Thǎńg and Nguyêñ Duy Tân
Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 83, Number 7
(2007), 93-98.
Abstract
In this note we establish the validity, in the case of unipotent group schemes over non-perfect fields, of an analog of Serre’s conjectures for algebraic groups, which relates properties of Galois (or flat) cohomology of unipotent group schemes to finite extensions of non-perfect fields. We also establish an interesting property of Russell’s defining equations of connected smooth one-dimensional unipotent groups over a field $k$.
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Permanent link to this document: http://projecteuclid.org/euclid.pja/1200672007
Digital Object Identifier: doi:10.3792/pjaa.83.93
Mathematical Reviews number (MathSciNet): MR2361418
Zentralblatt MATH identifier: 1190.11028
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