Nous obtenons un algorithme pour le calcul explicite des valeurs des rayons de convergence spectrales non solubles des solutions dʼun module différentiel sur un point de type 2, 3 ou 4 de la droite affine de Berkovich.
We obtain an algorithm computing explicitly the values of the non-solvable spectral radii of convergence of the solutions of a differential module over a point of type 2, 3 or 4 of the Berkovich affine line.
Accepté le :
Publié le :
Andrea Pulita 1
@article{CRMATH_2013__351_5-6_167_0, author = {Andrea Pulita}, title = {An algorithm computing non-solvable spectral radii of \protect\emph{p}-adic differential equations}, journal = {Comptes Rendus. Math\'ematique}, pages = {167--171}, publisher = {Elsevier}, volume = {351}, number = {5-6}, year = {2013}, doi = {10.1016/j.crma.2013.02.017}, language = {en}, }
Andrea Pulita. An algorithm computing non-solvable spectral radii of p-adic differential equations. Comptes Rendus. Mathématique, Volume 351 (2013) no. 5-6, pp. 167-171. doi : 10.1016/j.crma.2013.02.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.02.017/
[1] Gilles Christol, Structure de Frobénius des équations différentielles p-adiques, in: Groupe dʼÉtude dʼAnalyse Ultramétrique, 3e année (1975/1976), Fasc. 2, Marseille-Luminy, 1976, Exp. No. J5, Secrétariat Math., Paris, 1977, p. 7, MR 0498578 (58#16673).
[2] The radius of convergence function for first order differential equations, Advances in Non-Archimedean Analysis, Contemp. Math., vol. 551, Amer. Math. Soc., Providence, RI, 2011, pp. 71-89 (MR 2882390)
[3] Modules différentiels sur des couronnes, Ann. Inst. Fourier (Grenoble), Volume 44 (1994) no. 3, pp. 663-701 MR MR1303881 (96f:12008)
[4] Équations différentielles à points singuliers réguliers, Lecture Notes in Math., vol. 163, Springer-Verlag, Berlin, 1970 MR MR0417174 (54#5232)
[5] A simple algorithm for cyclic vectors, Amer. J. Math., Volume 109 (1987) no. 1, pp. 65-70 MR MR878198 (88b:13001)
[6] p-Adic Differential Equations, Cambridge Stud. Adv. Math., vol. 125, Cambridge Univ. Press, 2010
[7] Andrea Pulita, Small connections are cyclic, available at http://www.math.univ-montp2.fr/~pulita/Publications/Small-Connections.pdf.
[8] Rank one solvable p-adic differential equations and finite abelian characters via Lubin–Tate groups, Math. Ann., Volume 337 (2007) no. 3, pp. 489-555 (MR MR2274542)
[9] Andrea Pulita, The convergence Newton polygon of a p-adic differential equation I: Affinoid domains of the Berkovich affine line, preprint, 2012, 44 pp., . | arXiv
[10] Radii of convergence and index for p-adic differential operators, Trans. Amer. Math. Soc., Volume 333 (1992) no. 2, pp. 769-785 MR 1066451 (92m:12015)
Cité par Sources :
Commentaires - Politique