Théorie de Kummer-Artin-Schreier et applications

Noriyuki Suwa; Tsutomu Sekiguchi

Journal de théorie des nombres de Bordeaux (1995)

  • Volume: 7, Issue: 1, page 177-189
  • ISSN: 1246-7405

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Suwa, Noriyuki, and Sekiguchi, Tsutomu. "Théorie de Kummer-Artin-Schreier et applications." Journal de théorie des nombres de Bordeaux 7.1 (1995): 177-189. <http://eudml.org/doc/247649>.

@article{Suwa1995,
author = {Suwa, Noriyuki, Sekiguchi, Tsutomu},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {group schemes; Kummer-Artin-Schreier theory; nonramified cyclic extensions of a local ring; arithmetic schemes},
language = {fre},
number = {1},
pages = {177-189},
publisher = {Université Bordeaux I},
title = {Théorie de Kummer-Artin-Schreier et applications},
url = {http://eudml.org/doc/247649},
volume = {7},
year = {1995},
}

TY - JOUR
AU - Suwa, Noriyuki
AU - Sekiguchi, Tsutomu
TI - Théorie de Kummer-Artin-Schreier et applications
JO - Journal de théorie des nombres de Bordeaux
PY - 1995
PB - Université Bordeaux I
VL - 7
IS - 1
SP - 177
EP - 189
LA - fre
KW - group schemes; Kummer-Artin-Schreier theory; nonramified cyclic extensions of a local ring; arithmetic schemes
UR - http://eudml.org/doc/247649
ER -

References

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  1. [1] P. Furtwängler, Über die Reziprozitätsgesetze der l-ten Potenzreste in algebraischen Zahl-körpern, wenn l eine ungerage Primzahl bedeutet, Math. Ann.58 (1904), 1-50. Zbl34.0236.02
  2. [2] ____, Allgemeiner Existenzbeweis für den Klassenkörper eines bebliegen Zahlkölpers, Math. Ann.63 (1907), 1-37. JFM37.0243.02
  3. [3] L.N. Childs, The group of unramified Kummer extensions of prime degree, Proc. London Math. Soc.35 (1977), 407-422. Zbl0374.13002MR485821
  4. [4] K. Kato and S. Saito, Global class field theory of arithmetic schemes, Contemporary Math.55 (1986), 255-331. Zbl0614.14001MR862639
  5. [5] H.W. Leopoldt, Zur Struktur der l-Klassengruppe galoisscher Zahlkôrper, J. Reine Angew. Math. 199 (1958), 165-174. Zbl0082.25402MR96633
  6. [6] 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
  7. [7] T. Sekiguchi and N. Suwa, Théorie de Kummer-Artin-Schreier, C. R. Acad. Sci. Paris312 (1991), 417-420. Zbl0743.14030MR1096623
  8. [8] ____, Théories de Kummer-Artin-Schreier-Witt, C. R. Acad. Sci. Paris319 (1994),105-110. Zbl0845.14023MR1288386
  9. [9] ____, Unified Kummer-Artin-Schreier-Witt sequences, (en préparation). 
  10. [10] W.C. Waterhouse, A unified Kummer-Artin-Schreier sequence, Math. Ann.277 (1987), 447-451. Zbl0608.12026MR891585
  11. [SGA 1] A. Grothendieck, Revêtements étales et groupe fondamental, Lecture Notes in Math224 (1971). MR354651
  12. [SGA 2] ____, Cohomologie local des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (1968), Masson, North-Holland. 
  13. [SGA 4] M. Artin, A. Grothendieck and J.-L. Verdier, Théorie des topos et cohomologie étale de schémas, Lecture Notes in Math.269, 270, 305 (1972/73). Zbl0234.00007

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