Différentielles non commutatives et théorie de Galois différentielle ou aux différences
André, Yves
Annales scientifiques de l'École Normale Supérieure, Tome 34 (2001), p. 685-739 / Harvested from Numdam
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     author = {Andr\'e, Yves},
     title = {Diff\'erentielles non commutatives et th\'eorie de Galois diff\'erentielle ou aux diff\'erences},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {34},
     year = {2001},
     pages = {685-739},
     doi = {10.1016/s0012-9593(01)01074-6},
     mrnumber = {1862024},
     zbl = {1010.12004},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/ASENS_2001_4_34_5_685_0}
}
André, Yves. Différentielles non commutatives et théorie de Galois différentielle ou aux différences. Annales scientifiques de l'École Normale Supérieure, Tome 34 (2001) pp. 685-739. doi : 10.1016/s0012-9593(01)01074-6. http://gdmltest.u-ga.fr/item/ASENS_2001_4_34_5_685_0/

[1] André Y., Quatre descriptions des groupes de Galois différentiels, Sém. d'algèbre de Paris 86/87, Lect. Notes in Math., 1296, Springer-Verlag, 1987, pp. 28-41. | Zbl 0651.12015

[2] André Y., Notes sur la théorie de Galois différentielle, Prépubl. IHES/M/89/49, 1989.

[3] André Y., Pour une théorie inconditionnelle des motifs, Publ. Math. Inst. Hautes Études Sci. 83 (1996) 5-49. | Numdam | MR 1423019 | Zbl 0874.14010

[4] Aomoto K., q-analogue of de Rham cohomology associated with Jackson integrals, Proc. Japan Acad. 66 (1990) 161-164. | MR 1078398 | Zbl 0718.33011

[5] Berthelot P., Ogus A., Notes on Crystalline Cohomology, Math. Notes, 21, Princeton Univ. Press, 1978. | MR 491705 | Zbl 0383.14010

[6] Bertrand D., Groupes algébriques et équations différentielles linéaires, Sém. Bourbaki, exp. 750, février 1992, Astérisque 206 (1992) 183-204. | Numdam | MR 1206068 | Zbl 0813.12004

[7] Beukers F., Differential Galois theory, in: Waldschmidt M., Moussa P., Luck J.M., Itzykson C. (Eds.), From Number Theory to Physics, Springer-Verlag, 1992. | MR 1221099 | Zbl 0813.12001

[8] Bialynicki-Birula , On Galois theory of fields with operators, Amer. J. Math. 84 (1962) 89-109. | MR 141663 | Zbl 0113.03203

[9] Bourbaki N., Algèbre, Masson, 1981, chapitres III, IV et X. | MR 643362

[10] Bourbaki N., Algèbre commutative, Masson, 1985, chapitre I.

[11] Bruguières A., Théorie tannakienne non commutative, Comm. Algebra 22 (14) (1994) 5817-5860. | MR 1298753 | Zbl 0808.18005

[12] Bryant R., Recent advances in the theory of holonomy, Sém. Bourbaki, exp. 861, juin 1999, Astérisque 266 (2000) 351-374. | Numdam | MR 1772679 | Zbl 1014.53029

[13] Cohn P., Free Rings and their Relations, London Math. Soc. Monogr., 2, Academic Press, 1971. | MR 371938 | Zbl 0232.16003

[14] Cohn P., Skew Field Constructions, Cambridge Univ. Press, 1977. | MR 463237 | Zbl 0355.16009

[15] Connes A., Géométrie non commutative, Interéditions, 1990. | MR 1079062 | Zbl 0745.46067

[16] Connes A., Non-Commutative Geometry, Academic Press, 1994.

[17] Demazure M., Gabriel P., Groupes algébriques 1, North-Holland, 1970.

[18] Deligne P., Le groupe fondamental de la droite projective moins trois points, in: Galois Groups over Q ¯, M.S.R.I. Publ., 16, 1989, pp. 79-297. | MR 1012168 | Zbl 0742.14022

[19] Deligne P., Catégories tannakiennes, Grothendieck Festschrift, 2, Birkhäuser P.M. 87, 1990, pp. 111-198. | Zbl 0727.14010

[20] Deligne P., Milne J., Tannakian categories, Lect. Notes in Math., 900, Springer-Verlag, 1982, pp. 101-228. | Zbl 0477.14004

[21] Dubois-Violette M., Masson T., On the first order operators in bimodules, Lett. Math. Phys. 37 (1996) 464-474. | MR 1401049 | Zbl 0868.58009

[22] Dubois-Violette M., Some aspects of noncommutative differential geometry, Contemporary Math., 203, 1997, pp. 145-157. | Zbl 0876.58001

[23] Duval A., Lemmes de Hensel et factorisation formelle pour les opérateurs aux différences, Funkcial. Ekvac. 26 (1983) 349-368. | MR 748022 | Zbl 0543.12018

[24] Ekedahl T., Foliations and inseparable morphisms, Proc. Symp. Pure Math. 46 (1987) 139-149. | MR 927978 | Zbl 0659.14018

[25] Fahim A., Extensions galoisiennes d'algèbres différentielles, C. R. Acad. Sci. Paris, Série A 314 (1992) 1-4. | MR 1149627 | Zbl 0748.12004

[26] Gasper G., Rahman M., Basic Hypergeometric Series, Cambridge Univ. Press, 1990. | MR 1052153 | Zbl 0695.33001

[27] Hellegouarch Y., Galois calculus and Carlitz exponentials, in: Goss D., Hayes D., Rosen M. (Eds.), The Arithmetic of Function Fields, de Gruyter, 1992, pp. 33-50. | MR 1196510 | Zbl 0794.11025

[28] Karoubi M., Homologie cyclique et K-théorie, Astérisque, 149, Soc. Math. France, 1987. | MR 913964 | Zbl 0648.18008

[29] Karoubi M., Formes différentielles non commutatives et cohomologie à coefficients arbitraires, Trans. Amer. Math. Soc. 347 (11) (1995) 4277-4299. | MR 1316853 | Zbl 0852.55009

[30] Katz N., Nilpotent connections and the monodromy theorem. Applications of a result of Turrittin, Publ. Math. Inst. Hautes Études Sci. 39 (1970) 175-232. | Numdam | MR 291177 | Zbl 0221.14007

[31] Katz N., Exponential Sums and Differential Equations, Annals of Math. Studies, 124, Princeton, 1990. | MR 1081536 | Zbl 0731.14008

[32] Kobayashi S., Nomizu K., Foundations of Differential Geometry, Interscience I, 1963. | MR 152974 | Zbl 0119.37502

[33] Kolchin E., Algebraic matrix groups and the Picard-Vessiot theory of linear ordinary differential equations, Ann. of Math. 49 (1948) 1-42. | Zbl 0037.18701

[34] Laksov D., Thorup A., These are the differentials of order n, Trans. Amer. Math. Soc. 351 (4) (1999) 1293-1353. | MR 1458328 | Zbl 0920.13023

[35] Levelt A., Differential Galois theory and tensor products, Indag. Math. N.S. 1 (1990) 439-450. | MR 1106091 | Zbl 0731.12003

[36] Lichnerowicz A., Théorie globale des connexions et des groupes d'holonomie, Cremona, 1955. | Zbl 0116.39101

[37] Mathieu O., Classification des algèbres de Lie simples, Sém. Bourbaki, exp. 858, mars 1999, Astérisque 266 (2000) 245-286. | Numdam | MR 1772676 | Zbl 0990.17008

[38] Mourad J., Linear connections in noncommutative geometry, Class. Quant. Grav. 12 (1995) 965-974. | MR 1330296 | Zbl 0822.58006

[39] Nuss P., Noncommutative descent and non-abelian cohomology, 12 (1997) 23-74. | MR 1466623 | Zbl 0884.18015

[40] Praagman C., The formal classification of linear difference operators, Proc. Kon. Ned. Ac. Wet. Ser. A 86 (1983) 249-261. | MR 705431 | Zbl 0519.39003

[41] Saavedra Rivano N., Catégories tannakiennes, Lect. Notes in Math., 256, Springer-Verlag, 1972. | MR 338002 | Zbl 0241.14008

[42] Sauloy J., Matrice de connexion d'un système aux q-différences confluant vers un système différentiel de matrices de monodromie, C. R. Acad. Sci. Paris, Série I 328 (1999) 155-160. | MR 1669074 | Zbl 0919.39004

[43] Serre J.-P., Gèbres, L'Ens. Math. 39 (1993) 33-85. | MR 1225256 | Zbl 0810.16039

[44] Suzuki , General formulation of quantum analysis, Rev. Math. Physics 11 (2) (1999) 243-265. | MR 1681198 | Zbl 0930.46059

[45] Tannaka T., Über der Dualitätssatz der nichtkommutative topologischen Gruppen, Tôhoku Math. J. 45 (1939) 1-12. | JFM 64.0362.01

[46] Tarasov V., Varchenko A., Geometry of q-Hypergeometric Functions, Quantum Affine Algebras and Elliptic Quantum Groups, Astérisque, 246, Soc. Math. France, 1997. | MR 1646561 | Zbl 0938.17012

[47] Van Der Put M., Differential equations in characteristic p, Compositio Math. 97 (1995) 227-251. | Numdam | MR 1355126 | Zbl 0861.12004

[48] Van Der Put M., Singer M., Galois Theory of Difference Equations, Lect. Notes Math., 1666, Springer-Verlag, 1997. | MR 1480919 | Zbl 0930.12006

[49] Warner F., Foundations of Differentiable Manifolds and Lie Groups, Graduate Texts in Math., 94, Springer-Verlag, 1971. | MR 295244 | Zbl 0516.58001