Geodesic
NONHOLONOMIC SIMPLE D-MODULES FROM SIMPLE DERIVATIONS
Glasgow mathematical journal, Tome 49 (2007) no. 1, pp. 11-21

Voir la notice de l'article provenant de la source Cambridge University Press

We give new examples of affine sufaces whose rings of coordinates are d-simple and use these examples to construct simple nonholonomic D-modules over these surfaces.
DOI : 10.1017/S0017089507003370
Mots-clés : Primary: 13N15, 13N10, Secondary: 16S32 
COUTINHO, S. C. NONHOLONOMIC SIMPLE D-MODULES FROM SIMPLE DERIVATIONS. Glasgow mathematical journal, Tome 49 (2007) no. 1, pp. 11-21. doi: 10.1017/S0017089507003370
@article{10_1017_S0017089507003370,
     author = {COUTINHO, S. C.},
     title = {NONHOLONOMIC {SIMPLE} {D-MODULES} {FROM} {SIMPLE} {DERIVATIONS}},
     journal = {Glasgow mathematical journal},
     pages = {11--21},
     year = {2007},
     volume = {49},
     number = {1},
     doi = {10.1017/S0017089507003370},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003370/}
}
TY  - JOUR
AU  - COUTINHO, S. C.
TI  - NONHOLONOMIC SIMPLE D-MODULES FROM SIMPLE DERIVATIONS
JO  - Glasgow mathematical journal
PY  - 2007
SP  - 11
EP  - 21
VL  - 49
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003370/
DO  - 10.1017/S0017089507003370
ID  - 10_1017_S0017089507003370
ER  - 
%0 Journal Article
%A COUTINHO, S. C.
%T NONHOLONOMIC SIMPLE D-MODULES FROM SIMPLE DERIVATIONS
%J Glasgow mathematical journal
%D 2007
%P 11-21
%V 49
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003370/
%R 10.1017/S0017089507003370
%F 10_1017_S0017089507003370

[1] 1.Archer, J., Derivations on commutative rings and projective modules over skew polynomial rings, PhD thesis, Leeds University (1981). Google Scholar

[2] 2.Brumatti, P., Lequain, Y. and Levcovitz, D., Differential simplicity in polynomial rings and algebraic independence of power series, J. London Math. Soc. (2) 68 (2003), 615–630. Google Scholar | DOI

[3] 3.Coutinho, S. C., A primer of algebraic D-modules, London Mathematical Society Student Texts 33 (Cambridge University Press, 1995). Google Scholar | DOI

[4] 4.Coutinho, S. C., d-simple rings and simple D-modules, Math. Proc. Cambridge Phil. Soc. 125 (1999), 405–415. Google Scholar | DOI

[5] 5.Coutinho, S. C., On the differential simplicity of polynomial rings, J. Algebra 264 (2003), 442–468. Google Scholar | DOI

[6] 6.Coutinho, S. C., Indecomposable non-holonomic D-modules in dimension 2, Proc. Edinburgh Math. Soc. (2) 46 (2003), 341–355. Google Scholar | DOI

[7] 7.Coutinho, S. C., Non-holonomic irreducible D-modules over complete intersections, Proc. Amer. Math. Soc. 131 (2003), 83–86. Google Scholar | DOI

[8] 8.Coutinho, S. C. and Menasché, L.Schechter, Algebraic solutions of holomorphic foliations: an algorithmic approach, J. Symbolic Computation 41 (5) (2006), 603–618. Google Scholar | DOI

[9] 9.Doering, A. M., Lequain, Y. and Ripoll, C. C., Differential simplicity and cyclic maximal left ideals of the Weyl algebra A (K), Glasgow Math. J. 48 (2006), 269–274. Google Scholar | DOI

[10] 10.Jordan, D., Differentiably simple rings with no invertible derivatives, Quart. J. Math. Oxford Ser. 2, 32 (1981), 417–424. Google Scholar | DOI

[11] 11.Jouanolou, J. P., Equations de Pfaff algébriques Lecture Notes in Mathematics No. 708 (Springer-Verlag, 1979). Google Scholar | DOI

[12] 12.Goodearl, K. R. and Warfield, R. B., An introduction to noncommutative noetherian rings, London Mathematical Society Texts 16 (Cambridge University Press, 1989). Google Scholar

[13] 13.Maciejewski, A., Moulin-Ollagnier, J. and Nowicki, A., Simple quadratic derivations in two variables, Comm. Algebra 29 (2001), 619–638. Google Scholar | DOI

[14] 14.Mc Connell, J. C. and Robson, J. C., Noncommutative Noetherian rings (John Wiley & Sons, Chichester, 1987); revised edition by the American Mathematical Society, Providence, 2001. Google Scholar

[15] 15.Mendes, L. G., Algebraic foliations without algebraic solutions, An. Acad. bras. Ci. 69 (1997), 11–13. Google Scholar

[16] 16.Nowicki, A., An example of a simple derivation in two variables, preprint. Google Scholar

[17] 17.Shioda, T., On the Picard number of a complex projective variety, Ann. Scient. Éc. Norm. Sup., 4e série, 14 (1981), 303–321. Google Scholar | DOI

Cité par Sources :