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July 2007 On an analog of Serre’s conjectures, Galois cohomology and defining equation of unipotent algebraic groups
Nguyêñ Quôć Thǎńg, Nguyêñ Duy Tân
Proc. Japan Acad. Ser. A Math. Sci. 83(7): 93-98 (July 2007). DOI: 10.3792/pjaa.83.93

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 $k$.

Citation

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Nguyêñ Quôć Thǎńg. Nguyêñ Duy Tân. "On an analog of Serre’s conjectures, Galois cohomology and defining equation of unipotent algebraic groups." Proc. Japan Acad. Ser. A Math. Sci. 83 (7) 93 - 98, July 2007. https://doi.org/10.3792/pjaa.83.93

Information

Published: July 2007
First available in Project Euclid: 18 January 2008

zbMATH: 1190.11028
MathSciNet: MR2361418
Digital Object Identifier: 10.3792/pjaa.83.93

Subjects:
Primary: 11E72
Secondary: 12F05 , 12F15 , 20G10

Keywords: Galois cohomology , Serre’s conjectures , unipotent groups

Rights: Copyright © 2007 The Japan Academy

Vol.83 • No. 7 • July 2007
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