Hiroshima Mathematical Journal

Artin-Schreier-Witt extensions and normal bases

Noriyuki Suwa

Full-text: Open access

Abstract

We establish the Artin-Schreier-Witt theory in connection with the unit group scheme of a group algebra, following a method presented by Serre in Groupes algébriques et corps de classes. The argument is developed not only over a field but also over a ring, as generally as possible.

Article information

Source
Hiroshima Math. J., Volume 42, Number 3 (2012), 325-354.

Dates
First available in Project Euclid: 11 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1355238372

Digital Object Identifier
doi:10.32917/hmj/1355238372

Mathematical Reviews number (MathSciNet)
MR3050125

Zentralblatt MATH identifier
1279.13015

Subjects
Primary: 13B05: Galois theory
Secondary: 14L15: Group schemes 12G05: Galois cohomology [See also 14F22, 16Hxx, 16K50]

Keywords
Artin-Schreier-Witt extensions Witt vectors Artin-Hasse exponetial series

Citation

Suwa, Noriyuki. Artin-Schreier-Witt extensions and normal bases. Hiroshima Math. J. 42 (2012), no. 3, 325--354. doi:10.32917/hmj/1355238372. https://projecteuclid.org/euclid.hmj/1355238372


Export citation

References

  • H. Chu, S. J. Hu, M. C. Kang, B. E. Kunyavskii, Noether's problem and the unramified Brauer group for groups of order 64, Int. Math. Res. Not. IMRN (2010) 2329–2366.
  • M. Demazure, P. Gabriel, Groupes algébriques, Tome I, Masson & Cie, Editeur, Paris; North-Holland Publishing, Amsterdam, 1970.
  • B. Dwork, On the rationality of the zeta function of an algebraic variety, Amer. J. Math. 82 (1960), 631–648.
  • M. Hazewinkel, Formal groups and applications, Academic Press. New York, 1978.
  • H. F. Kreimer, M. Takeuchi, Hopf algebras and Galois extensions of an algebra, Indiana Univ. Math. J. 30 (1981) 675–692.
  • H. Kuniyoshi, On a problem of Chevalley, Nagoya Math. J. 8 (1955) 65–67.
  • T. Sekiguchi, N. Suwa, A note on extensions of algebraic and formal groups IV, Tôhoku Math. J. 53 (2001) 203–240.
  • J. P. Serre, Groupes algébriques et corps de classes, Hermann, Paris, 1959
  • N. Suwa, Around Kummer theories, RIMS Kôkyûroku Bessatsu B12 (2009) 115–148.
  • Y. Tsuno, Degenerations of the Kummer sequence in characteristic $p>0$, J. Théor. Nombres Bordeaux 22 (2010) 199–237.
  • Y. Tsuno, Normal basis problem for torsors under a finite flat group scheme, RIMS Kôkyûroku Bessatsu B25 (2009) 53–74.
  • M. Amano, On the Cartier duality of certain finite group schemes of order $p^n$, Tokyo J. Math. 33 (2010) 117–127.