On the structure of the group scheme ℤ [ ℤ / p n ] ×

Tsutomu Sekiguchi; Noriyuki Suwa

Compositio Mathematica (1995)

  • Volume: 97, Issue: 1-2, page 253-271
  • ISSN: 0010-437X

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Sekiguchi, Tsutomu, and Suwa, Noriyuki. "On the structure of the group scheme $\mathbb {Z}[\mathbb {Z} / p^n]^\times $." Compositio Mathematica 97.1-2 (1995): 253-271. <http://eudml.org/doc/90378>.

@article{Sekiguchi1995,
author = {Sekiguchi, Tsutomu, Suwa, Noriyuki},
journal = {Compositio Mathematica},
keywords = {unit group of group algebra; group scheme; cyclic group of prime power order; Kummer-Artin-Schreier-Witt theories},
language = {eng},
number = {1-2},
pages = {253-271},
publisher = {Kluwer Academic Publishers},
title = {On the structure of the group scheme $\mathbb \{Z\}[\mathbb \{Z\} / p^n]^\times $},
url = {http://eudml.org/doc/90378},
volume = {97},
year = {1995},
}

TY - JOUR
AU - Sekiguchi, Tsutomu
AU - Suwa, Noriyuki
TI - On the structure of the group scheme $\mathbb {Z}[\mathbb {Z} / p^n]^\times $
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 97
IS - 1-2
SP - 253
EP - 271
LA - eng
KW - unit group of group algebra; group scheme; cyclic group of prime power order; Kummer-Artin-Schreier-Witt theories
UR - http://eudml.org/doc/90378
ER -

References

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  1. [1] S. Annantharaman, 'Schémas en groupes, espaces homogénes et espaces algébriques sur une base de dimension 1', Bull. Soc. Math. France, Mémoire 33 (1973). Zbl0286.14001MR335524
  2. [2] M. Demazure and P. Gabriel, Groupes algébriques, Tome 1, Masson-North-Holland, 1970. Zbl0203.23401
  3. [3] G. Karpilovsky, Unit groups of group rings, Longman Scientific and Technical, 1989. Zbl0687.16010MR1042757
  4. [4] F. Oort, Commutative group schemes, Lecture Notes in Math.Springer, Vol. 15, 1966. Zbl0216.05603MR213365
  5. [5] T. Sekiguchi, 'On the deformation of Witt groups to toriII' J. of Algebra138 (1991) 273-297. Zbl0735.14033MR1102811
  6. [6] T. Sekiguchi and N. Suwa, 'A case of extensions of group schemes over a discrete valuation ring', Tsukuba J. Math.14 (1990) 459-487. Zbl0755.14014MR1085212
  7. [7] T. Sekiguchi and N. Suwa, 'Théorie de Kummer-Artin-Schreier', C.R. Acad. Sci.Paris, 312 (1991) 417-420. Zbl0743.14030MR1096623
  8. [8] T. Sekiguchi and N. Suwa, 'Théories de Kummer-Artin-Schreier-Witt ', C.R. Acad. Sci.Paris319 (1994) 105-110. Zbl0845.14023MR1288386
  9. [9] T. Sekiguchi and N. Suwa, 'Théorie de Kummer-Artin-Schreier et applications', (to appear in the Proceedings of Journées Arithmétiques Bordeaux1993). Zbl0920.14023MR1413576
  10. [10] T. Sekiguchi and N. Suwa, 'On the unified Kummer-Artin-Schreier-Witt theory', Preprint series, Chuo-Math.41 (1994). Zbl0845.14023MR1288386
  11. [11] T. Sekiguchi and N. Suwa, 'On the unit group schemes of commutative group algebras' (in preparation). Zbl0755.14014
  12. [12] T. Sekiguchi, F. Oort and N. Suwa, 'On the deformation of Artin-Schreier to Kummer', Ann. Scient. Ec. Normale Sup.22 (1989) 345-375. Zbl0714.14024MR1011987
  13. [13] J-P. Serre, Groupes algébriques et corps de classes, Hermann, 1959. Zbl0097.35604
  14. [14] W.C. Waterhouse, 'A unified Kummer-Artin-Schreier sequence', Math. Ann.277 (1987) 447-451. Zbl0608.12026MR891585
  15. [15] W.C. Waterhouse, Introduction to affine group schemes, Graduate Texts in Math, Vol. 66, Springer, 1979. Zbl0442.14017MR547117
  16. [16] W.C. Waterhouse and B. Weisfeiler, 'One-dimensional affine group schemes ', J. of Algebra66 (1980) 550-568. Zbl0452.14013MR593611
  17. [17] A. Grothendieck et A. Dieudonné, Eléments de géométrie algébriques I, Springer, 1971. Zbl0203.23301

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