Degeneration of the Kummer sequence in characteristic p > 0

Yuji Tsuno[1]

  • [1] Department of Mathematics Chuo University 1-13-27 Kasuga Bunkyo-ku, Tokyo 112-8551, JAPAN

Journal de Théorie des Nombres de Bordeaux (2010)

  • Volume: 22, Issue: 1, page 219-257
  • ISSN: 1246-7405

Abstract

top
We study a deformation of the Kummer sequence to the radicial sequence over an 𝔽 p -algebra, which is somewhat dual for the deformation of the Artin-Schreier sequence to the radicial sequence, studied by Saidi. 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.

How to cite

top

Tsuno, Yuji. "Degeneration of the Kummer sequence in characteristic $p&gt;0$." Journal de Théorie des Nombres de Bordeaux 22.1 (2010): 219-257. <http://eudml.org/doc/116398>.

@article{Tsuno2010,
abstract = {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 Saidi. 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.},
affiliation = {Department of Mathematics Chuo University 1-13-27 Kasuga Bunkyo-ku, Tokyo 112-8551, JAPAN},
author = {Tsuno, Yuji},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {1},
pages = {219-257},
publisher = {Université Bordeaux 1},
title = {Degeneration of the Kummer sequence in characteristic $p&gt;0$},
url = {http://eudml.org/doc/116398},
volume = {22},
year = {2010},
}

TY - JOUR
AU - Tsuno, Yuji
TI - Degeneration of the Kummer sequence in characteristic $p&gt;0$
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2010
PB - Université Bordeaux 1
VL - 22
IS - 1
SP - 219
EP - 257
AB - 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 Saidi. 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.
LA - eng
UR - http://eudml.org/doc/116398
ER -

References

top
  1. M. Demazure and P. Gabriel, Groupes algébriques, Tome I. Masson & Cie, Editeur, Paris; North-Holland Publishing, Amsterdam, 1970. Zbl0203.23401MR302656
  2. A. Grothendieck, Le groupe de Brauer. Dix exposés sur la cohomologie des schémas, 46–188. North-Holland, 1968. MR244269
  3. B. Mazur, L. Roberts, Local Euler Characteristics. Invent. math. 9 (1970), 201–234. Zbl0191.19202MR258844
  4. M. Saidi, On the degeneration of étale ℤ / p ℤ and ℤ / p 2 ℤ -torsors in equal characteristic p &gt; 0 . Hiroshima. Math. J. 37 (2007), 315–341. Zbl1155.14025MR2345371
  5. T. Sekiguchi and N. Suwa, Théorie de Kummer-Artin-Schreier et applications. J. Théor. Nombres Bordeaux 7 (1995), 177–189. Zbl0920.14023MR1413576
  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. Zbl0714.14024MR1011987
  7. J. P. Serre, Groupes algébriques et corps de classes. Hermann, Paris, 1959. Zbl0097.35604MR103191
  8. R. P. Stanley, Enumerative Combinatorics, vol. 1. Cambridge Stud. Adv. Math. vol. 49, Cambridge University Press, Cambridge, 1997. Zbl0889.05001MR1442260
  9. N. Suwa, Twisted Kummer and Kummer-Artin-Schreier theories. Tôhoku Math. J. 60 (2008), 183–218. Zbl1145.13005MR2428860
  10. N. Suwa, Around Kummer theories. RIMS Kôkyûroku Bessatsu B12 (2009), 115–148. Zbl1219.14058
  11. J. Tate and F. Oort, Group scheme of prime order. Ann. Sci. Éc. Norm. Sup. (4) 3 (1970), 1–21. Zbl0195.50801MR265368
  12. W. C. Waterhouse, Introduction to affine group schemes. Springer, 1979. Zbl0442.14017MR547117
  13. W. C. Waterhouse, A unified Kummer-Artin-Schreier sequence. Math. Ann. 277 (1987), 447–451. Zbl0608.12026MR891585
  14. W. C. Waterhouse and B. Weisfeiler, One-dimensional affine group schemes. J. Algebra 66 (1980), 550–568. Zbl0452.14013MR593611

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.