Algebraic properties of a class of <i>p</i>-adic exponentials

Daniele Chinellato

doi:10.1016/j.crma.2006.12.001

Algebraic Geometry/Ordinary Differential Equations

Algebraic properties of a class of p-adic exponentials

Presented by: Michel Raynaud

Daniele Chinellato ¹

¹ Dip. di Matematica, Via Trieste 63, 35121 Padova, Italy

Comptes Rendus. Mathématique, Volume 344 (2007) no. 3, pp. 187-190.

Abstract
Résumé

In this Note we give an algebraic construction of a class of p-adic exponentials of Artin–Hasse type which are convergent in the disk $D^{-} (0, 1)$ . Moreover we have a control for the field of coefficients of power series that defines such functions. Such objects were used by Christol and Robba to calculate the irregularity of a rank 1 p-adic differential operator, under the restriction of spherical completeness for the field of coefficients, and recently by Pulita, in order to classify the same equations.

Dans cette Note nous donnons une construction algébrique d'une classe d'exponentielles p-adiques du type d'Artin–Hasse qui sont convergentes dans le disque $D^{-} (0, 1)$ . Nous avons d'ailleurs un contrôle des coefficients de la série entière qui définit de telles fonctions. De tels objets ont été employés par Christol et Robba pour calculer l'irrégularité d'un opérateur différentiel p-adique d'ordre 1, sous la restriction que le champ des coefficients soit sphériquement complet, et récemment par Pulita, afin de classifier les mêmes équations.

Received: 2006-05-11
Accepted: 2006-12-04
Published online: 2007-01-05

DOI: 10.1016/j.crma.2006.12.001

Author's affiliations:

Daniele Chinellato ¹

¹ Dip. di Matematica, Via Trieste 63, 35121 Padova, Italy

@article{CRMATH_2007__344_3_187_0,
     author = {Daniele Chinellato},
     title = {Algebraic properties of a class of \protect\emph{p}-adic exponentials},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {187--190},
     publisher = {Elsevier},
     volume = {344},
     number = {3},
     year = {2007},
     doi = {10.1016/j.crma.2006.12.001},
     language = {en},
}

TY  - JOUR
AU  - Daniele Chinellato
TI  - Algebraic properties of a class of p-adic exponentials
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 187
EP  - 190
VL  - 344
IS  - 3
PB  - Elsevier
DO  - 10.1016/j.crma.2006.12.001
LA  - en
ID  - CRMATH_2007__344_3_187_0
ER  -

%0 Journal Article
%A Daniele Chinellato
%T Algebraic properties of a class of p-adic exponentials
%J Comptes Rendus. Mathématique
%D 2007
%P 187-190
%V 344
%N 3
%I Elsevier
%R 10.1016/j.crma.2006.12.001
%G en
%F CRMATH_2007__344_3_187_0

Daniele Chinellato. Algebraic properties of a class of p-adic exponentials. Comptes Rendus. Mathématique, Volume 344 (2007) no. 3, pp. 187-190. doi : 10.1016/j.crma.2006.12.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.12.001/

References
Cited by

[1] N. Bourbaki Elements of Mathematics, Algebra II, Springer-Verlag, 1990

[2] N. Bourbaki Eléments de Mathématiques, Chapitre IX, Algèbre Commutative, Masson, 1983

[3] G. Christol; P. Robba Equations différentielles p-adiques, Hermann, 1994

[4] B. Dwork Generalized Hypergeometric Functions, Clarendon Press, 1990

[5] B. Dwork, Manuscript

[6] B. Dwork; G. Gerotto; F.J. Sullivan An Introduction to G-Functions, Annals of Mathematics Studies, vol. 133, Princeton Univ. Press, 1994

[7] M. Lazard Commutative Formal Groups, Lecture Notes in Mathematics, vol. 443, Springer-Verlag, 1975

[8] S. Matsuda Local Indices of p-adic differential operators corresponding to Artin–Schreier–Witt coverings, Duke Math. J., Volume 77 (1995), pp. 607-625

[9] A. Pulita, Rank one solvable p-adic differential equations and finite Abelian characters via Lubin–Tate groups, Math. Ann., in press

[10] P. Robba Indice d'un opérateur différentiel p-adique IV. Cas de systèmes, Ann. Inst. Fourier, Volume 35 (1985), pp. 13-55

Cited by Sources:

Comments - Policy