Nous étudions une déformation de la suite de Kummer à la suite radicielle sur une -algèbre, qui est duale en un sens pour la déformation de la suite d’Artin-Schreier à la suite radicielle, étudiée par Saidi. Nous examinons aussi quelques relations entre nos suites et l’immersion d’un schéma en groupes commutatifs, fini et plat dans un schéma en groupes commutatifs, lisse, affine et connexe, construite par Grothendieck.
We study a deformation of the Kummer sequence to the radicial sequence over an -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.
@article{JTNB_2010__22_1_219_0,
author = {Tsuno, Yuji},
title = {Degeneration of the {Kummer} sequence in characteristic $p>0$},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {219--257},
publisher = {Universit\'e Bordeaux 1},
volume = {22},
number = {1},
year = {2010},
doi = {10.5802/jtnb.713},
zbl = {1237.14055},
mrnumber = {2675882},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jtnb.713/}
}
TY - JOUR AU - Tsuno, Yuji TI - Degeneration of the Kummer sequence in characteristic $p>0$ JO - Journal de théorie des nombres de Bordeaux PY - 2010 SP - 219 EP - 257 VL - 22 IS - 1 PB - Université Bordeaux 1 UR - http://www.numdam.org/articles/10.5802/jtnb.713/ DO - 10.5802/jtnb.713 LA - en ID - JTNB_2010__22_1_219_0 ER -
%0 Journal Article %A Tsuno, Yuji %T Degeneration of the Kummer sequence in characteristic $p>0$ %J Journal de théorie des nombres de Bordeaux %D 2010 %P 219-257 %V 22 %N 1 %I Université Bordeaux 1 %U http://www.numdam.org/articles/10.5802/jtnb.713/ %R 10.5802/jtnb.713 %G en %F JTNB_2010__22_1_219_0
Tsuno, Yuji. Degeneration of the Kummer sequence in characteristic $p>0$. Journal de théorie des nombres de Bordeaux, Tome 22 (2010) no. 1, pp. 219-257. doi : 10.5802/jtnb.713. http://www.numdam.org/articles/10.5802/jtnb.713/
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