Relations among analytic functions. II
Annales de l'Institut Fourier, Tome 37 (1987) no. 2, pp. 49-77.

Cet article fait suite à “Relations among analytic functions I”, Ann. Inst. Fourier, 37, fasc. 1, [pp. 187-239]. On réduit à la semicontinuité des invariants locaux le problème de trouver des solutions 𝒞∞ de systèmes d’équations dans lesquelles interviennent division et composition par des fonctions analytiques. On démontre la semicontinuité dans plusieurs cas généraux : dans la catégorie algébrique, pour les morphismes “réguliers”, et pour les holomorphismes de modules sur un morphisme fini.

This is a sequel to “Relations among analytic functions I”, Ann. Inst. Fourier, 37, fasc. 1, [pp. 187-239]. We reduce to semicontinuity of local invariants the problem of finding 𝒞∞ solutions to systems of equations involving division and composition by analytic functions. We prove semicontinuity in several general cases : in the algebraic category, for “regular” mappings, and for module homomorphisms over a finite mapping.

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     author = {Bierstone, Edward and Milman, P. D.},
     title = {Relations among analytic functions. {II}},
     journal = {Annales de l'Institut Fourier},
     pages = {49--77},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {37},
     number = {2},
     year = {1987},
     doi = {10.5802/aif.1086},
     mrnumber = {88g:32013b},
     zbl = {0611.32003},
     language = {en},
     url = {https://numdam.org/articles/10.5802/aif.1086/}
}
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Bierstone, Edward; Milman, P. D. Relations among analytic functions. II. Annales de l'Institut Fourier, Tome 37 (1987) no. 2, pp. 49-77. doi : 10.5802/aif.1086. https://numdam.org/articles/10.5802/aif.1086/

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