Tsuno, Yuji Degeneration of the Kummer sequence in characteristic \(p>0\). (English) Zbl 1237.14055 J. Théor. Nombres Bordx. 22, No. 1, 219-257 (2010). Summary: We study a deformation of the Kummer sequence to the radicial sequence over an \(\mathbb{F}_p\)-algebra, which is somewhat dual for the deformation of the Artin-Schreier sequence to the radicial sequence, studied by M. Saïdi [Hiroshima Math. J. 37, No. 2, 315–341 (2007; Zbl 1155.14025)]. We also discuss some relations between our sequences and the embedding of a finite flat commutative group scheme into a connected smooth affine commutative group schemes, constructed by Grothendieck. MSC: 14L15 Group schemes 12G05 Galois cohomology Citations:Zbl 1155.14025 PDFBibTeX XMLCite \textit{Y. Tsuno}, J. Théor. Nombres Bordx. 22, No. 1, 219--257 (2010; Zbl 1237.14055) Full Text: DOI EuDML References: [1] M. Demazure and P. Gabriel, Groupes algébriques, Tome I. Masson & Cie, Editeur, Paris; North-Holland Publishing, Amsterdam, 1970. · Zbl 0203.23401 [2] A. Grothendieck, Le groupe de Brauer. Dix exposés sur la cohomologie des schémas, 46-188. North-Holland, 1968. · Zbl 0192.57801 [3] B. Mazur, L. Roberts, Local Euler Characteristics. Invent. math. 9 (1970), 201-234. · Zbl 0191.19202 [4] M. Saidi, On the degeneration of étale \(\mathbb{Z}/p\mathbb{Z}\) and \(\mathbb{Z}/{p^2}\mathbb{Z} \)-torsors in equal characteristic \(p>0\). Hiroshima. Math. J. 37 (2007), 315-341. · Zbl 1155.14025 [5] T. Sekiguchi and N. Suwa, Théorie de Kummer-Artin-Schreier et applications. J. Théor. Nombres Bordeaux 7 (1995), 177-189. · Zbl 0920.14023 [6] T. Sekiguchi, F. Oort and N. Suwa, On the deformation of Artin-Schreier to Kummer. Ann. Sci. École Norm. Sup. (4) 22 (1989), 345-375. · Zbl 0714.14024 [7] J. P. Serre, Groupes algébriques et corps de classes. Hermann, Paris, 1959. · Zbl 0097.35604 [8] R. P. Stanley, Enumerative Combinatorics, vol. 1. Cambridge Stud. Adv. Math. vol. 49, Cambridge University Press, Cambridge, 1997. · Zbl 0889.05001 [9] N. Suwa, Twisted Kummer and Kummer-Artin-Schreier theories. Tôhoku Math. J. 60 (2008), 183-218. · Zbl 1145.13005 [10] N. Suwa, Around Kummer theories. RIMS Kôkyûroku Bessatsu B12 (2009), 115-148. · Zbl 1219.14058 [11] J. Tate and F. Oort, Group scheme of prime order. Ann. Sci. Éc. Norm. Sup. (4) 3 (1970), 1-21. · Zbl 0195.50801 [12] W. C. Waterhouse, Introduction to affine group schemes. Springer, 1979. · Zbl 0442.14017 [13] W. C. Waterhouse, A unified Kummer-Artin-Schreier sequence. Math. Ann. 277 (1987), 447-451. · Zbl 0608.12026 [14] W. C. Waterhouse and B. Weisfeiler, One-dimensional affine group schemes. J. Algebra 66 (1980), 550-568. · Zbl 0452.14013 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.