Christol, Gilles Systèmes différentiels linéaires \(p\)-adiques, structure de Frobenius faible. (French) Zbl 0459.12020 Bull. Soc. Math. Fr. 109, 83-122 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 Documents MSC: 12H25 \(p\)-adic differential equations 12J25 Non-Archimedean valued fields 11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.) Keywords:p-adic analytic functions; infinite product decomposition; Frobenius operation on linear differential equations Citations:Zbl 0304.14014 PDFBibTeX XMLCite \textit{G. Christol}, Bull. Soc. Math. Fr. 109, 83--122 (1981; Zbl 0459.12020) Full Text: DOI Numdam EuDML References: [1] CHRISTOL . - Structure de Frobenius des équations différentielles p-adiques, Groupe d’étude d’analyse ultramétrique , 3e année : Journées d’analyse ultram., Marseille. Luminy, 1976 , exposé J5. Numdam | Zbl 0352.12015 · Zbl 0352.12015 [2] DELIGNE . - Équations différentielles à points singuliers réguliers , Lecture notes in Math, n^\circ 163, 1970 , Springer, Berlin, Heidelberg, New York. MR 54 #5232 | Zbl 0244.14004 · Zbl 0244.14004 [3] DWORK . - On p-adic differential equations I , Bull. Soc. Math. Fr., Mémoire 39-40, 1974 , p. 27-37. Numdam | Zbl 0304.14014 · Zbl 0304.14014 [4] DWORK . - On p-adic differential equations II , Annals of Math., vol. 98, n^\circ 2, septembre 1973 , p. 366-376. MR 58 #27987b | Zbl 0304.14015 · Zbl 0304.14015 [5] DWORK-ROBBA . - On ordinary linear p-adic differential equations , Trans. Amer. Math Soc., vol. 231, n^\circ 1, 1977 . MR 56 #5562 | Zbl 0375.34010 · Zbl 0375.34010 [6] ESCASSUT . - Algèbre de Banach ultramétriques , Astérisque, 10, 1973 . MR 50 #6726 | Zbl 0289.12109 · Zbl 0289.12109 [7] KATZ . - Nilpotent connections and the monodromy theorem , Publ. Math I.H.E.S., vol. 39, 1970 , p. 355-432. Numdam | Zbl 0221.14007 · Zbl 0221.14007 [8] MANIN . - Moduli fuchsiani , Annali Scuola Norm. Sup. Pisa, Sér. III, vol. 19, 1965 , p. 113-126. Numdam | MR 31 #4815 | Zbl 0166.04301 · Zbl 0166.04301 [9] ROBBA . - Structure de Frobenius faible pour les équations différentielles du premier ordre . Groupe d’étude d’analyse ultramétrique, 2e année, 1974 - 1975 , n^\circ 20. Numdam | Zbl 0331.12104 · Zbl 0331.12104 [10] SERRE . - Corps locaux , Publ. de l’Institut de Math de l’université de Nancago-VIII, 1968 . MR 50 #7096 · Zbl 1095.11504 [11] SPERBER . - p-adic hypergeometric functions and their cohomology , Duke Math J., vol. 44, 1977 , p. 535-589. Article | MR 57 #16307 | Zbl 0408.12025 · Zbl 0408.12025 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.