@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] 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] Éléments de mathématique. Algèbre commutative. Chapitre IX. Anneaux locaux noethériens complets. Springer, Berlin, 2006. | Zbl 1103.13003
.[BR10] 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
and .[Car67a] 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] 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] 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] 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
and .[Gou97] p-adic numbers. Universitext. Springer-Verlag, Berlin, 1997. | MR 1488696 | Zbl 0786.11001
.[Haz86] 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] Witt vectors. I. In Handbook of algebra. Vol. 6, 319–472. Elsevier/North-Holland, Amsterdam, 2009. | MR 2553661 | Zbl 1221.13036
.[Hes10] The big de Rham-Witt complex, Acta Math., 214(1) :135-207, 2015. | MR 3316757
.[Kat12] Witt Vectors and a question of Keating and Rudnick. Int. Math. Res. Not. IMRN 2013. no. 16, 3613–3638. | MR 3090703
.[Loe96] Principe de Boyarsky et -modules. Math. Ann., 306(1) :125–157, 1996. | MR 1405321 | Zbl 0911.14012
.[LS88] Applications of rigid cohomology to arithmetic geometry. PhD thesis, University of Minnesota, 1988. | MR 2636618
.[Man10] Cyclotomy and analytic geometry over . In Quanta of maths, 385–408, Clay Math. Proc., 11, Amer. Math. Soc., Providence, RI, 2010. | MR 2732059 | Zbl 1231.14018
.[Mat95] 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] P-adic theory of exponential sums on the affine line. Thesis (Ph. D.) - University of Florida, 2010, 44 pp. ProQuest LLC. | MR 2771526
.[Mum66] 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] 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.
and .[Pul06] Thèse de doctorat. Équations différentielles p-adiques d’ordre un et applications. 2006 www.imj-prg.fr/theses//pdf/2006/andrea_pulita/pdf.
.[Pul07] 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] 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] 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] 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] A course in p-adic analysis, volume 198 of Graduate Texts in Mathematics. Springer-Verlag, New York, 2000. | MR 1760253 | Zbl 0947.11035
.[Rül07a] 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] 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] Boyarsky principle for -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
.