nLab Kummer-Artin-Schreier-Witt exact sequence

Idea

A joint generalization of the concept of Kummer exact sequence and of Artin-Schreier exact sequence. A review is in Mezard-Romagny-Tossici 11, section 1.

The case $n =1$ (Kummer-Artin-Schreier sequence) is due to (Waterhouse 87) and independently (Sekiguchi-Oort-Suwa 89). The general case is due to (Sekiguchi-Suwa 94, Sekiguchi-Suwa 99, Sekiguchi-Suwa 01) and accordingly also referred to as Sekiguchi-Suwa theory (Mezard-Romagny-Tossici 11).

Related concepts

• ring of Witt vectors

• exponential exact sequence

References

• William Waterhouse, A unified Kummer-Artin-Schreier sequence, Mathematische Annalen 1987, Volume 277, Issue 3, pp 447-451 (publisher)

• T. Sekiguchi, F. Oort and N. Suwa, On the deformation of Artin-Schreier to Kummer, Ann. Scient. Éc. Norm. Sup., 4e série 22 (1989), 345–375

• T. Sekiguchi, N. Suwa, Théories de Kummer-Artin-Schreier-Witt, C. R. Acad. Sci. Paris, 319 Série I, (1994), 105–110.

• T. Sekiguchi, N. Suwa, On the Unified Kummer-Artin-Schreier-Witt theory, Prépublications du laboratoire de Mathématiques Pures de Bordeaux, Prépublication n◦ 111 (1999).

• T. Sekiguchi, N. Suwa, A note on extensions of algebraic and formal groups IV, Kummer-Artin- Schreier-Witt theory of degree p2, Tohoku Math. J. 53 (2001), 203–240.

• Kazuyoshi Tsuchiya, On the descriptions of $\mathbb{Z}/p^2\mathbb{Z}$-Torsors by the Kummer-Artin-Schreier-Witt theory, Tokyo J. of Math. Volume 26, Number 1 (2003), 147-177. (ProjectEuclid)

• Ariane Mézard, Matthieu Romagny, Dajano Tossici, Sekiguchi-Suwa theory revisited (arXiv:1104.2222)