Separation, factorization and finite sheaves on Nash manifolds
Compositio Mathematica, Tome 103 (1996) no. 1, pp. 31-62. 
@article{CM_1996__103_1_31_0,
     author = {Coste, Michel and Ruiz, Jes\'us M. and Shiota, Masahiro},
     title = {Separation, factorization and finite sheaves on {Nash} manifolds},
     journal = {Compositio Mathematica},
     pages = {31--62},
     publisher = {Kluwer Academic Publishers},
     volume = {103},
     number = {1},
     year = {1996},
     mrnumber = {1404997},
     zbl = {0885.14029},
     language = {en},
     url = {http://www.numdam.org/item/CM_1996__103_1_31_0/}
}
TY  - JOUR
AU  - Coste, Michel
AU  - Ruiz, Jesús M.
AU  - Shiota, Masahiro
TI  - Separation, factorization and finite sheaves on Nash manifolds
JO  - Compositio Mathematica
PY  - 1996
SP  - 31
EP  - 62
VL  - 103
IS  - 1
PB  - Kluwer Academic Publishers
UR  - http://www.numdam.org/item/CM_1996__103_1_31_0/
LA  - en
ID  - CM_1996__103_1_31_0
ER  - 
%0 Journal Article
%A Coste, Michel
%A Ruiz, Jesús M.
%A Shiota, Masahiro
%T Separation, factorization and finite sheaves on Nash manifolds
%J Compositio Mathematica
%D 1996
%P 31-62
%V 103
%N 1
%I Kluwer Academic Publishers
%U http://www.numdam.org/item/CM_1996__103_1_31_0/
%G en
%F CM_1996__103_1_31_0
Coste, Michel; Ruiz, Jesús M.; Shiota, Masahiro. Separation, factorization and finite sheaves on Nash manifolds. Compositio Mathematica, Tome 103 (1996) no. 1, pp. 31-62. http://www.numdam.org/item/CM_1996__103_1_31_0/

[An] D'Angelo, J.: Orders of contact of real and complex subvarieties, Illinois J. Math. 26 (1982) 41-51. | MR | Zbl

[Ar] Artin, M.: Algebraic approximation of structures over complete local rings, Publ. Math. I.H.E.S. 36 (1969) 23-58. | Numdam | MR | Zbl

[BeTo] Benedetti, R. and Tognoli, A.: On real algebraic vector bundles, Bull. Sc. Math. 104 (1980) 89-102. | MR | Zbl

[BaTo] Beretta, L. and Tognoli, A.: Nash sets and global equations, Bolletino U.M.I. (7) 4-A (1990) 31-44. | MR | Zbl

[BoCoRo] Bochnak, J., Coste, M. and Roy, M-F.: Géométrie algébrique réelle, Springer 1987. | MR | Zbl

[CoRzSh] Coste, M., Ruiz, J.M. and Shiota, M.: Approximation in compact Nash manifolds, Amer. J. Math. 117 (1995) 1-23. | MR | Zbl

[Ef1] Efroymson, G.: Nash rings in planar domains, Trans. Amer. Math. Soc. 249 (1979) 435-445. | MR | Zbl

[Ef2] Efroymson, G.: The extension theorem for Nash functions, in: Géométrie algébrique réelle et formes quadratiques, 343-357, Lecture Notes in Math. 959, Springer 1982. | MR | Zbl

[EkTn] El Khadiri, A. and Tougeron, J-C.: Familles noethériennes de modules sur k[[X]] et applications, to appear in Bull. Sc. Math. | MR | Zbl

[FoLoRa] Fortuna, E., Lojasiewicz, S. and Raimondo, M.: Algebricité de germes analytiques, J. reine angew. Math. 374 (1987) 208-213. | MR | Zbl

[GuRo] Gunning, R.C. and Rossi, H.: Analytic functions of several complex variables, Prentice-Hall 1965. | MR | Zbl

[Hd] Hubbard, J.: On the cohomology of Nash sheaves, Topology 11 (1972) 265-270. | MR | Zbl

[Hr] Huber, R.: Isoalgebraische Räume, thesis, Regensburg 1984.

[Kn] Knebusch, M.: Isoalgebraic geometry: first steps, in: Sém. Delange-Pisot-Poitou (1980-81) 215-220Progress in Math. 22, Birkhäuser 1982. | MR | Zbl

[MoRa] Mora, F. and Raimondo, M.: Sulla fattorizzazzione analitica delle funzioni di Nash, Le Matematiche 37 (1982) 251-256. | MR | Zbl

[Mo] Mostowski, T.: Some properties of the ring of Nash functions, Ann. Scuola Norm. Sup. Pisa 3 (1976) 245-266. | Numdam | MR | Zbl

[Pe] Pecker, D.: On Efroymson's extension theorem for Nash functions, J. Pure Appl. Algebra 37 (1985) 193-203. | MR | Zbl

[Qu] Quarez, R.: The idempotency of the real spectrum implies the extension theorem for Nash functions, preprint, Rennes 1994. | MR | Zbl

[RzSh] Ruiz, J.M. and Shiota, M.: On global Nash functions, Ann. scient. Éc. Norm. Sup. 27 (1994) 103-124. | Numdam | MR | Zbl

[Sh1]Shiota, M.: On the unique factorization of the ring of Nash functions, Publ. RIMS Kyoto Univ. 17 (1981) 363-369. | MR | Zbl

[Sh2] Shiota, M.: Nash manifolds, Lecture Notes in Math. 1269, Springer 1987. | MR | Zbl

[Sh3] Shiota, M.: Extension et factorisation de fonctions de Nash C∞, C. R. Acad. Sci. Paris 308 (1989) 253-256. | Zbl

[Th] Thom, R.: Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954) 17-86. | MR | Zbl

[TaTo] Tancredi, A. and Tognoli, A.: On the extension of Nash functions, Math. Ann. 288 (1990) 595-604. | MR | Zbl

[To] Tognoli, A.: Algebraic geometry and Nash functions, Institutiones Math. 3, Academic Press 1978. | MR | Zbl

[WhBr] Whitney, H. and Bruhat, F.: Quelques propriétés fondamentales des ensembles analytiques réels, Comment. Math. Helvet. 33 (1959) 132-160. | MR | Zbl