Des π-exponentielles I : vecteurs de Witt annulés par Frobenius et algorithme de (leur) rayon de convergence
Rodolphe, Richard
Rendiconti del Seminario Matematico della Università di Padova, Tome 134 (2015), p. 125-158 / Harvested from Numdam
Publié le : 2015-01-01
@article{RSMUP_2015__133__125_0,
     author = {Rodolphe, Richard},
     title = {Des $\pi $-exponentielles I : vecteurs de Witt annul\'es par Frobenius et algorithme de (leur) rayon de convergence},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {134},
     year = {2015},
     pages = {125-158},
     mrnumber = {3354948},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/RSMUP_2015__133__125_0}
}
Rodolphe, Richard. Des $\pi $-exponentielles I : vecteurs de Witt annulés par Frobenius et algorithme de (leur) rayon de convergence. Rendiconti del Seminario Matematico della Università di Padova, Tome 134 (2015) pp. 125-158. http://gdmltest.u-ga.fr/item/RSMUP_2015__133__125_0/

[Bal10] Francesco Baldassarri. Continuity of the radius of convergence of differential equations on p-adic analytic curves. Invent. Math., 182(3) :513–584, 2010. | MR 2737705 | Zbl 1221.14027

[Bou06] N. Bourbaki. Éléments de mathématique. Algèbre commutative. Chapitre IX. Anneaux locaux noethériens complets. Springer, Berlin, 2006. | Zbl 1103.13003

[BR10] Matthew Baker and Robert Rumely. Potential theory and dynamics on the Berkovich projective line, volume 159 of Mathematical Surveys and Monographs. Amer. Math. Soc., Providence, RI, 2010. | MR 2599526 | Zbl 1196.14002

[Car67a] Pierre Cartier. Groupes formels associés aux anneaux de Witt généralisés. C. R. Acad. Sci. Paris Sér. A-B, 265 :A49–A52, 1967. | MR 218361 | Zbl 0168.27501

[Car67b] Pierre Cartier. Modules associés à un groupe formel commutatif. Courbes typiques. C. R. Acad. Sci. Paris Sér. A-B, 265 :A129–A132, 1967. | MR 218362 | Zbl 0168.27502

[Chr11] Gilles Christol. The radius of convergence function for first order differential equations. In Advances in non-Archimedean analysis, 71–89, Contemp. Math., 551, Amer. Math. Soc., Providence, RI, 2011. | MR 2882390 | Zbl 1238.12006

[DR80] B. Dwork and P. Robba. Effective p-adic bounds for solutions of homogeneous linear differential equations. Trans. Amer. Math. Soc., 259(2) :559–577, 1980. | MR 567097 | Zbl 0439.12016

[Gou97] Fernando Q. Gouvêa. p-adic numbers. Universitext. Springer-Verlag, Berlin, 1997. | MR 1488696 | Zbl 0786.11001

[Haz86] Michiel Hazewinkel. Three lectures on formal groups. In Lie algebras and related topics (Windsor, Ont., 1984), 51–67, CMS Conf. Proc., 5, Amer. Math. Soc., Providence, RI, 1986. | MR 832194 | Zbl 0596.14035

[Haz09] Michiel Hazewinkel. Witt vectors. I. In Handbook of algebra. Vol. 6, 319–472. Elsevier/North-Holland, Amsterdam, 2009. | MR 2553661 | Zbl 1221.13036

[Hes10] Lars Hesselholt. The big de Rham-Witt complex, Acta Math., 214(1) :135-207, 2015. | MR 3316757

[Kat12] Nicholas M. Katz. Witt Vectors and a question of Keating and Rudnick. Int. Math. Res. Not. IMRN 2013. no. 16, 3613–3638. | MR 3090703

[Loe96] François Loeser. Principe de Boyarsky et 𝒟 -modules. Math. Ann., 306(1) :125–157, 1996. | MR 1405321 | Zbl 0911.14012

[LS88] Bernard Le Stum. Applications of rigid cohomology to arithmetic geometry. PhD thesis, University of Minnesota, 1988. | MR 2636618

[Man10] Yuri I. Manin. Cyclotomy and analytic geometry over 𝔽 1 . In Quanta of maths, 385–408, Clay Math. Proc., 11, Amer. Math. Soc., Providence, RI, 2010. | MR 2732059 | Zbl 1231.14018

[Mat95] Shigeki Matsuda. Local indices of p-adic differential operators corresponding to Artin-Schreier-Witt coverings. Duke Math. J., 77(3) :607–625, 1995. | MR 1324636 | Zbl 0849.12013

[Mor10] Yuri Morofushi. P-adic theory of exponential sums on the affine line. Thesis (Ph. D.) - University of Florida, 2010, 44 pp. ProQuest LLC. | MR 2771526

[Mum66] David Mumford. Lectures on curves on an algebraic surface. With a section by G. M. Bergman. Annals of Mathematics Studies, No. 59. Princeton University Press, Princeton, N.J., 1966. | MR 209285 | Zbl 1079.14002

[PP12] Jérôme Poineau and Andrea Pulita. The convergence Newton polygon of a p-adic differential equation II: Continuity and finiteness on Berkovich curves. prépublication, 2012 htpp://arxiv.org/abs/1209.3663.

[Pul06] Andrea Pulita. Thèse de doctorat. Équations différentielles p-adiques d’ordre un et applications. 2006 www.imj-prg.fr/theses//pdf/2006/andrea_pulita/pdf.

[Pul07] Andrea Pulita. Rank one solvable p-adic differential equations and finite abelian characters via Lubin-Tate groups. Math. Ann., 337(3) :489–555, 2007. | MR 2274542 | Zbl 1125.12001

[Pul12] Andrea Pulita. The convergence Newton polygon of a p-adic differential equation I: Affinoid domains of the Berkovich affine line. prépublication, 2012. http://arxiv.org/abs/1208.5850. | MR 3372170

[Rob84] Philippe Robba. Index of p-adic differential operators. III. Application to twisted exponential sums. Astérisque, (119-120) :7, 191–266, 1984. | MR 773094 | Zbl 0548.12015

[Rob86] Philippe Robba. Une introduction naïve aux cohomologies de Dwork. Introductions aux cohomologies p-adiques (Luminy, 1984). Mém. Soc. Math. France (N.S.), (23) :5, 61–105, 1986. | Numdam | MR 865812 | Zbl 0623.14005

[Rob00] Alain M. Robert. A course in p-adic analysis, volume 198 of Graduate Texts in Mathematics. Springer-Verlag, New York, 2000. | MR 1760253 | Zbl 0947.11035

[Rül07a] Kay Rülling. Erratum to: “The generalized de Rham-Witt complex over a field is a complex of zero-cycles” J. Algebraic Geom., 16(4) :793–795, 2007. | MR 2357690 | Zbl 1122.14007

[Rül07b] Kay Rülling. The generalized de Rham-Witt complex over a field is a complex of zero-cycles. J. Algebraic Geom., 16(1) :109–169, 2007. | MR 2257322 | Zbl 1122.14006

[Ter04] Tomohide Terasoma. Boyarsky principle for 𝒟 -modules and Loeser’s conjecture. In Geometric aspects of Dwork theory. Vol. I, II, 909–930. Walter de Gruyter, Berlin, 2004. | MR 2099092 | Zbl 1065.12002