@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}, pages = {125--158}, publisher = {Seminario Matematico of the University of Padua}, volume = {133}, year = {2015}, mrnumber = {3354948}, language = {fr}, url = {http://www.numdam.org/item/RSMUP_2015__133__125_0/} }
TY - JOUR AU - Rodolphe, Richard TI - Des $\pi $-exponentielles I : vecteurs de Witt annulés par Frobenius et algorithme de (leur) rayon de convergence JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2015 SP - 125 EP - 158 VL - 133 PB - Seminario Matematico of the University of Padua UR - http://www.numdam.org/item/RSMUP_2015__133__125_0/ LA - fr ID - RSMUP_2015__133__125_0 ER -
%0 Journal Article %A Rodolphe, Richard %T Des $\pi $-exponentielles I : vecteurs de Witt annulés par Frobenius et algorithme de (leur) rayon de convergence %J Rendiconti del Seminario Matematico della Università di Padova %D 2015 %P 125-158 %V 133 %I Seminario Matematico of the University of Padua %U http://www.numdam.org/item/RSMUP_2015__133__125_0/ %G fr %F 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 133 (2015), pp. 125-158. http://www.numdam.org/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 | Zbl
.[Bou06] Éléments de mathématique. Algèbre commutative. Chapitre IX. Anneaux locaux noethériens complets. Springer, Berlin, 2006. | Zbl
.[BR10] Potential theory and dynamics on the Berkovich projective line, volume 159 of Mathematical Surveys and Monographs. Amer. Math. Soc., Providence, RI, 2010. | MR | Zbl
and .[Car67a] Groupes formels associés aux anneaux de Witt généralisés. C. R. Acad. Sci. Paris Sér. A-B, 265 :A49–A52, 1967. | MR | Zbl
.[Car67b] Modules associés à un groupe formel commutatif. Courbes typiques. C. R. Acad. Sci. Paris Sér. A-B, 265 :A129–A132, 1967. | MR | Zbl
.[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 | Zbl
.[DR80] Effective p-adic bounds for solutions of homogeneous linear differential equations. Trans. Amer. Math. Soc., 259(2) :559–577, 1980. | MR | Zbl
and .[Gou97] p-adic numbers. Universitext. Springer-Verlag, Berlin, 1997. | MR | Zbl
.[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 | Zbl
.[Haz09] Witt vectors. I. In Handbook of algebra. Vol. 6, 319–472. Elsevier/North-Holland, Amsterdam, 2009. | MR | Zbl
.[Hes10] The big de Rham-Witt complex, Acta Math., 214(1) :135-207, 2015. | MR
.[Kat12] Witt Vectors and a question of Keating and Rudnick. Int. Math. Res. Not. IMRN 2013. no. 16, 3613–3638. | MR
.[Loe96] Principe de Boyarsky et -modules. Math. Ann., 306(1) :125–157, 1996. | MR | Zbl
.[LS88] Applications of rigid cohomology to arithmetic geometry. PhD thesis, University of Minnesota, 1988. | MR
.[Man10] Cyclotomy and analytic geometry over . In Quanta of maths, 385–408, Clay Math. Proc., 11, Amer. Math. Soc., Providence, RI, 2010. | MR | Zbl
.[Mat95] Local indices of p-adic differential operators corresponding to Artin-Schreier-Witt coverings. Duke Math. J., 77(3) :607–625, 1995. | MR | Zbl
.[Mor10] P-adic theory of exponential sums on the affine line. Thesis (Ph. D.) - University of Florida, 2010, 44 pp. ProQuest LLC. | MR
.[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 | Zbl
.[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 | Zbl
.[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
.[Rob84] Index of p-adic differential operators. III. Application to twisted exponential sums. Astérisque, (119-120) :7, 191–266, 1984. | Numdam | MR | Zbl
.[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 | Zbl
.[Rob00] A course in p-adic analysis, volume 198 of Graduate Texts in Mathematics. Springer-Verlag, New York, 2000. | MR | Zbl
.[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 | Zbl
.[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 | Zbl
.[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 | Zbl
.