Residue currents and complexity problems
Elkadi, M. ; Yger, A.
Banach Center Publications, Tome 31 (1995), p. 173-186 / Harvested from The Polish Digital Mathematics Library
Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:262595
@article{bwmeta1.element.bwnjournal-article-bcpv31z1p173bwm,
     author = {Elkadi, M. and Yger, A.},
     title = {Residue currents and complexity problems},
     journal = {Banach Center Publications},
     volume = {31},
     year = {1995},
     pages = {173-186},
     zbl = {0831.32002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv31z1p173bwm}
}
Elkadi, M.; Yger, A. Residue currents and complexity problems. Banach Center Publications, Tome 31 (1995) pp. 173-186. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv31z1p173bwm/

[000] [Ai] L. A. Aizenberg and A. P. Yuzhakov, Integral Representation and Residues in Multidimensional Complex Analysis, Amer. Math. Soc., Providence, 1983.

[001] [Am] F. Amoroso, Bounds for the degrees in the membership test for a polynomial ideal, Acta Arith. 56 (1990), 19-24.

[002] [Am1] F. Amoroso, Tests d'appartenance d'après un théorème de J. Kollar, C. R. Acad. Sci. Paris Sér. I 309 (1989), 691-694. | Zbl 0703.13003

[003] [Am2] F. Amoroso, Membership problem, in: Diophantine Approximations and Transcendental Numbers, Luminy 1990, P. Philippon (ed.), Walter de Gruyter, Berlin, 1992, 15-37.

[004] [Am3] F. Amoroso, On a conjecture of C. Berenstein and A. Yger, in: Proc. MEGA 94, Progr. Math., Birkhäuser, to appear.

[005] [Am4] F. Amoroso, The membership problem for smooth ideals, Publ. Math. Univ. P. et M. Curie, to appear.

[006] [Am5] F. Amoroso, The membership problem for 'almost' complete intersection ideals, preprint.

[007] [At] M. F. Atiyah, Resolution of singularities and division of distributions, Comm. Pure Appl. Math. 23 (1970), 145-150. | Zbl 0188.19405

[008] [BaS] D. Bayer and M. Stillman, On the complexity of computing syzygies, J. Symbolic Comp. 6 (1988), 135-147. | Zbl 0667.68053

[009] [BGVY] C. A. Berenstein, R. Gay, A. Vidras and A. Yger, Residue Currents and Bézout Identities, Progr. Math. 114, Birkhäuser, 1993.

[010] [BT] C. A. Berenstein and B. A. Taylor, Interpolation problems in n with applications to harmonic analysis, J. Analyse Math. 38 (1980), 188-254. | Zbl 0464.42003

[011] [BY1] C. A. Berenstein and A. Yger, Bounds for the degrees in the division problem, Michigan Math. J. 37 (1990), 26-44.

[012] [BY2] C. A. Berenstein and A. Yger, Effective Bézout identities in [z1,...,zn], Acta Math. 166 (1991), 69-120. | Zbl 0724.32002

[013] [BY3] C. A. Berenstein and A. Yger, Une formule de Jacobi et ses conséquences, Ann. Sci. Ecole. Norm. Sup. 24 (1991), 363-377. | Zbl 0742.32004

[014] [BY4] C. A. Berenstein and A. Yger, Formules de représentation intégrale et problèmes de division, in: Diophantine Approximations and Transcendental Numbers, P. Philippon (ed.), Walter de Gruyter, Berlin, 1992, 15-37. | Zbl 0765.32002

[015] [BY5] C. A. Berenstein and A. Yger, Bounds for the division problem, in: Proc. Sympos. Pure Math. 52, part 1, Amer. Math. Soc., 1991, 22-28.

[016] [BGS1] J. B. Bost, H. Gillet et C. Soulé, Un analogue arithmétique du théorème de Bézout, C. R. Acad. Sci. Paris Sér. I 312 (1991), 845-848.

[017] [BGS2] J. B. Bost, H. Gillet et C. Soulé, Heights of projective varieties and positive Green forms, J. Amer. Math. Soc. 7 (1994), 903-1027. | Zbl 0973.14013

[018] [Br1] W. D. Brownawell, Bounds for the degrees in the Nullstellensatz, Ann. of Math. 126 (1987), 577-591. | Zbl 0641.14001

[019] [Br2] W. D. Brownawell, Local diophantine Nullstellen inequalities, J. Amer. Math. Soc. 1 (1988), 311-322. | Zbl 0651.10022

[020] [Br3] W. D. Brownawell, Distance to common zeros and lower bounds for polynomials, in: Diophantine Approximations and Transcendental Numbers, Luminy 1990, P. Philippon (ed.), Walter de Gruyter, Berlin, 1992, 51-64.

[021] [Br4] W. D. Brownawell, A prime power version of the Nullstellensatz, Michigan Math. J., to appear.

[022] [Elk1] M. Elkadi, Une version effective du théorème de Briançon-Skoda dans le cas algébrique discret, Acta Arith. 66 (1994), 201-220.

[023] [Elk2] M. Elkadi, Bornes pour les degrés et les hauteurs dans le problème de division, Michigan Math. J., to appear.

[024] [Fa] G. Faltings, Diophantine approximation on Abelian varieties, Ann. of Math. 133 (1991), 549-576. | Zbl 0734.14007

[025] [GH] P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley-Interscience, New York, 1978. | Zbl 0408.14001

[026] [GS] H. Gillet and C. Soulé, Arithmetic intersection theory, Publ. Math. I.H.E.S. 72 (1990), 93-174. | Zbl 0741.14012

[027] [HP] W. V. D. Hodge and D. Pedoe, An Introduction to Algebraic Geometry, 3 Volumes, Cambridge University Press, Cambridge, 1952.

[028] [Jac] C. G. J. Jacobi, Theoremata nova algebraica circa systema duarum aequationum inter duas variabiles propositarum, in: Gesammelte Werke, Band III, 285-294.

[029] [Ko] J. Kollár, Sharp effective Nullstellensatz, J. Amer. Math. Soc. 1 (1988), 963-975.

[030] [Ky] A. M. Kytmanov, A transformation formula for Grothendieck residues and some of its applications, Siberian Math. J. 1989, 495-499.

[031] [LT] J. Lipman and B. Teissier, Pseudorational local rings and a theorem of Briançon-Skoda about integral closures of ideals, Michigan Math. J. 28 (1981), 97-115. | Zbl 0464.13005

[032] [Mac] F. S. Macaulay, The Algebraic Theory of Modular Systems, Cambridge University Press, Cambridge, 1916.

[033] [MaM] E. Mayr and A. Meyer, The complexity of the word problem for commutative semigroups and polynomial ideals, Adv. in Math. 127 (1988), 305-329.

[034] [Ph1] P. Philippon, Critères pour l'indépendance algébrique, Publ. Math. I.H.E.S. 64 (1986), 5-52.

[035] [Ph2] P. Philippon, A propos du texte de W.D. Brownawell: 'Bounds for the degrees in the Nullstellensatz', Ann. of Math. 127 (1988), 367-371.

[036] [Ph3] P. Philippon, Dénominateurs dans le théorème des zéros de Hilbert, Acta Arith. 58 (1991), 1-25. | Zbl 0679.13010

[037] [Ph4] P. Philippon, Sur des hauteurs alternatives I, Math. Ann. 289 (1991), 255-283. | Zbl 0726.14017

[038] [Sk] H. Skoda, Application des techniques L2 à la théorie des idéaux d’une algèbre de fonctions holomorphes avec poids, Ann. Sci. Ecole. Norm. Sup. 5 (1972), 545-579. | Zbl 0254.32017

[039] [St] W. Stoll, About the value distribution of holomorphic maps into projective space, Acta Math. 123 (1969), 83-114. | Zbl 0177.11302

[040] [Ts] A. Tsikh, Multidimensional Residues and Their Applications, Transl. Math. Monographs, Amer. Math. Soc., 1992.

[041] [Weil] A. Weil, L'intégrale de Cauchy et les fonctions de plusieurs variables, Math. Ann. 111 (1935), 178-182. | Zbl 0011.12301

[042] [Y] A. Yger, Résidus, courants résiduels et courants de Green, in: Actes du Colloque de Géométrie Analytique, Paris VII, 1992, Travaux en Cours, Hermann, Paris, to appear.