Différentielles non commutatives et théorie de Galois différentielle ou aux différences
Annales scientifiques de l'École Normale Supérieure (2001)
- Volume: 34, Issue: 5, page 685-739
- ISSN: 0012-9593
Access Full Article
topHow to cite
topAndré, Yves. "Différentielles non commutatives et théorie de Galois différentielle ou aux différences." Annales scientifiques de l'École Normale Supérieure 34.5 (2001): 685-739. <http://eudml.org/doc/82555>.
@article{André2001,
author = {André, Yves},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {differential Galois group; holonomy group; Galois correspondence theorem},
language = {fre},
number = {5},
pages = {685-739},
publisher = {Elsevier},
title = {Différentielles non commutatives et théorie de Galois différentielle ou aux différences},
url = {http://eudml.org/doc/82555},
volume = {34},
year = {2001},
}
TY - JOUR
AU - André, Yves
TI - Différentielles non commutatives et théorie de Galois différentielle ou aux différences
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2001
PB - Elsevier
VL - 34
IS - 5
SP - 685
EP - 739
LA - fre
KW - differential Galois group; holonomy group; Galois correspondence theorem
UR - http://eudml.org/doc/82555
ER -
References
top- [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. Zbl0651.12015
- [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. Zbl0874.14010MR1423019
- [4] Aomoto K., q-analogue of de Rham cohomology associated with Jackson integrals, Proc. Japan Acad.66 (1990) 161-164. Zbl0718.33011MR1078398
- [5] Berthelot P., Ogus A., Notes on Crystalline Cohomology, Math. Notes, 21, Princeton Univ. Press, 1978. Zbl0383.14010MR491705
- [6] Bertrand D., Groupes algébriques et équations différentielles linéaires, Sém. Bourbaki, exp. 750, février 1992, Astérisque206 (1992) 183-204. Zbl0813.12004MR1206068
- [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. Zbl0813.12001MR1221099
- [8] Bialynicki-Birula, On Galois theory of fields with operators, Amer. J. Math.84 (1962) 89-109. Zbl0113.03203MR141663
- [9] Bourbaki N., Algèbre, Masson, 1981, chapitres III, IV et X. MR643362
- [10] Bourbaki N., Algèbre commutative, Masson, 1985, chapitre I.
- [11] Bruguières A., Théorie tannakienne non commutative, Comm. Algebra22 (14) (1994) 5817-5860. Zbl0808.18005MR1298753
- [12] Bryant R., Recent advances in the theory of holonomy, Sém. Bourbaki, exp. 861, juin 1999, Astérisque266 (2000) 351-374. Zbl1014.53029MR1772679
- [13] Cohn P., Free Rings and their Relations, London Math. Soc. Monogr., 2, Academic Press, 1971. Zbl0232.16003MR371938
- [14] Cohn P., Skew Field Constructions, Cambridge Univ. Press, 1977. Zbl0355.16009MR463237
- [15] Connes A., Géométrie non commutative, Interéditions, 1990. Zbl0745.46067MR1079062
- [16] Connes A., Non-Commutative Geometry, Academic Press, 1994.
- [17] Demazure M., Gabriel P., Groupes algébriques 1, North-Holland, 1970. Zbl0203.23401
- [18] Deligne P., Le groupe fondamental de la droite projective moins trois points, in: Galois Groups over , M.S.R.I. Publ., 16, 1989, pp. 79-297. Zbl0742.14022MR1012168
- [19] Deligne P., Catégories tannakiennes, Grothendieck Festschrift, 2, Birkhäuser P.M. 87, 1990, pp. 111–198. Zbl0727.14010
- [20] Deligne P., Milne J., Tannakian categories, Lect. Notes in Math., 900, Springer-Verlag, 1982, pp. 101–228. Zbl0477.14004
- [21] Dubois-Violette M., Masson T., On the first order operators in bimodules, Lett. Math. Phys.37 (1996) 464-474. Zbl0868.58009MR1401049
- [22] Dubois-Violette M., Some aspects of noncommutative differential geometry, Contemporary Math., 203, 1997, pp. 145–157. Zbl0876.58001
- [23] Duval A., Lemmes de Hensel et factorisation formelle pour les opérateurs aux différences, Funkcial. Ekvac.26 (1983) 349-368. Zbl0543.12018MR748022
- [24] Ekedahl T., Foliations and inseparable morphisms, Proc. Symp. Pure Math.46 (1987) 139-149. Zbl0659.14018MR927978
- [25] Fahim A., Extensions galoisiennes d'algèbres différentielles, C. R. Acad. Sci. Paris, Série A314 (1992) 1-4. Zbl0748.12004MR1149627
- [26] Gasper G., Rahman M., Basic Hypergeometric Series, Cambridge Univ. Press, 1990. Zbl0695.33001MR1052153
- [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. Zbl0794.11025MR1196510
- [28] Karoubi M., Homologie cyclique et K-théorie, Astérisque, 149, Soc. Math. France, 1987. Zbl0648.18008MR913964
- [29] Karoubi M., Formes différentielles non commutatives et cohomologie à coefficients arbitraires, Trans. Amer. Math. Soc.347 (11) (1995) 4277-4299. Zbl0852.55009MR1316853
- [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. Zbl0221.14007MR291177
- [31] Katz N., Exponential Sums and Differential Equations, Annals of Math. Studies, 124, Princeton, 1990. Zbl0731.14008MR1081536
- [32] Kobayashi S., Nomizu K., Foundations of Differential Geometry, Interscience I, 1963. Zbl0119.37502MR152974
- [33] Kolchin E., Algebraic matrix groups and the Picard–Vessiot theory of linear ordinary differential equations, Ann. of Math.49 (1948) 1-42. Zbl0037.18701
- [34] Laksov D., Thorup A., These are the differentials of order n, Trans. Amer. Math. Soc.351 (4) (1999) 1293-1353. Zbl0920.13023MR1458328
- [35] Levelt A., Differential Galois theory and tensor products, Indag. Math. N.S.1 (1990) 439-450. Zbl0731.12003MR1106091
- [36] Lichnerowicz A., Théorie globale des connexions et des groupes d'holonomie, Cremona, 1955. Zbl0116.39101
- [37] Mathieu O., Classification des algèbres de Lie simples, Sém. Bourbaki, exp. 858, mars 1999, Astérisque266 (2000) 245-286. Zbl0990.17008MR1772676
- [38] Mourad J., Linear connections in noncommutative geometry, Class. Quant. Grav.12 (1995) 965-974. Zbl0822.58006MR1330296
- [39] Nuss P., Noncommutative descent and non-abelian cohomology, 12 (1997) 23-74. Zbl0884.18015MR1466623
- [40] Praagman C., The formal classification of linear difference operators, Proc. Kon. Ned. Ac. Wet. Ser. A86 (1983) 249-261. Zbl0519.39003MR705431
- [41] Saavedra Rivano N., Catégories tannakiennes, Lect. Notes in Math., 256, Springer-Verlag, 1972. Zbl0241.14008MR338002
- [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 I328 (1999) 155-160. Zbl0919.39004MR1669074
- [43] Serre J.-P., Gèbres, L'Ens. Math.39 (1993) 33-85. Zbl0810.16039MR1225256
- [44] Suzuki, General formulation of quantum analysis, Rev. Math. Physics11 (2) (1999) 243-265. Zbl0930.46059MR1681198
- [45] Tannaka T., Über der Dualitätssatz der nichtkommutative topologischen Gruppen, Tôhoku Math. J.45 (1939) 1-12. JFM64.0362.01
- [46] Tarasov V., Varchenko A., Geometry of q-Hypergeometric Functions, Quantum Affine Algebras and Elliptic Quantum Groups, Astérisque, 246, Soc. Math. France, 1997. Zbl0938.17012MR1646561
- [47] van der Put M., Differential equations in characteristic p, Compositio Math.97 (1995) 227-251. Zbl0861.12004MR1355126
- [48] van der Put M., Singer M., Galois Theory of Difference Equations, Lect. Notes Math., 1666, Springer-Verlag, 1997. Zbl0930.12006MR1480919
- [49] Warner F., Foundations of Differentiable Manifolds and Lie Groups, Graduate Texts in Math., 94, Springer-Verlag, 1971. Zbl0516.58001MR295244
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.