Rings of separated power series

Lipshitz, Leonard

Rings of separated power series and quasi-affinoid geometry, Astérisque, no. 264 (2000), pp. 3-108.

@incollection{AST_2000__264__3_0,
     author = {Lipshitz, Leonard},
     title = {Rings of separated power series},
     booktitle = {Rings of separated power series and quasi-affinoid geometry},
     editor = {Lipschitz, L\'eonard and Robinson, Zachary},
     series = {Ast\'erisque},
     pages = {3--108},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {264},
     year = {2000},
     mrnumber = {1758887},
     zbl = {0957.32011},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2000__264__3_0/}
}

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%E Robinson, Zachary
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Lipshitz, Leonard. Rings of separated power series, dans Rings of separated power series and quasi-affinoid geometry, Astérisque, no. 264 (2000), pp. 3-108. http://archive.numdam.org/item/AST_2000__264__3_0/

Bibliographie
Cité par

[1] W. Bartenwerfer. - Der allgemeine Kontinuitätssatz für $k$ -meromorphe Funktionen im Dizylinder. Math. Ann., 191 (1971) 196-234. | DOI | EuDML | MR | Zbl

[2] W. Bartenwerfer. - Die Beschränktheit der Stückzahl der Fasern $K$ -analytischer Abbildungen. J. reine angew. Math., 416 (1991) 49-70. | EuDML | MR | Zbl

[3] V. Berkovich. - Spectral Theory and Analytic Geometry Over Non-Archimedean Fields. Math. Surveys and Monographs, Vol. 33, A.M.S., Providence, 1990. | MR | Zbl

[4] S. Bosch. - Orthonormalbasen in der nichtarchimedischen Funktionentheorie. Manuscripta Math., 1 (1969) 35-57. | DOI | EuDML | MR | Zbl

[5] S. Bosch. - Eine bemerkenswerte Eigenschaft der formellen Fasern affinoider Räume. Math. Ann., 229 (1977) 25-45. | DOI | EuDML | MR | Zbl

[6] S. Bosch, U. Güntzer and R. Remmert. - Non-Archimedean Analysis. Springer-Verlag, 1984. | DOI | MR | Zbl

[7] N. Bourbaki. - Éléments de Mathématiques, XV. Espaces Vectoriels Topologiques, Chapter 1. Hermann, 1953. | Zbl

[8] N. Bourbaki. - Algèbre Commutative III. Hermann, 1961. | Zbl

[9] J. Denef and L. Van Den Dries. - $p$ -adic and real subanalytic sets. Ann. Math., 128, (1988) 79-138. | DOI | MR | Zbl

[10] J. Fresnel and M. Van Der Put. - Géométrie Analytique Rigide et Applications. Birkhäuser, 1981. | MR | Zbl

[11] J. Fresnel and M. Van Der Put. - Localisation formelle et Groupe de Picard. Ann. Inst. Fourier (Grenoble), 33 (1983) 19-82. | DOI | EuDML | Numdam | MR | Zbl

[12] T. Gardener. - Local flattening in rigid analytic geometry. Preprint. | DOI | MR | Zbl

[13] T. Gardener and H. Schoutens. - Flattening and subanalytic sets in rigid analytic geometry. Preprint. | DOI | MR | Zbl

[14] H. Grauert and R. Remmert. - Über die Methode der diskret bewerteten Ringe in der nicht-Archimedischen Analysis. Invent. Math., 2 (1966) 87-133. Begründung. | DOI | EuDML | MR | Zbl

[15] H. Hironaka. - Subanalytic Sets, in Number Theory, Algebraic Geometry and Commutative Algebra in honor of Y. Akizuki, Kinokuniya, 1973, 453-493. | MR | Zbl

[16] L. Lipshitz. - Isolated points on fibers of affinoid varieties. J. reine angew. Math., 384 (1988) 208-220. | EuDML | MR | Zbl

[17] L. Lipshitz. - Rigid subanalytic sets. Amer. J. Math., 115 (1993) 77-108. | DOI | MR | Zbl

[18] L. Lipshitz and Z. Robinson. - Rigid subanalytic subsets of the line and the plane. Amer. J. Math., 118 (1996) 493-527. | DOI | MR | Zbl

[19] L. Lipshitz and Z. Robinson. - Rigid subanalytic subsets of curves and surfaces. To appear in J. London Math. Soc. | MR | Zbl

[20] L. Lipshitz and Z. Robinson. - One-dimensional fibers of rigid subanalytic sets. J. Symbolic Logic, 63 (1998) 83-88. | DOI | MR | Zbl

[21] L. Lipshitz and Z. Robinson. - Rigid subanalytic sets II. Manuscript. | Zbl

[22] L. Lipshitz and Z. Robinson. - Quasi-affinoid varieties. This volume.

[23] L. Lipshitz and Z. Robinson. - Model completeness and subanalytic sets. This volume.

[24] A. Macintrye. - On definable subsets of $p$ -adic fields. J. Symbolic Logic, 41 (1976) 605-610. | DOI | MR | Zbl

[25] H. Matsumura. - Commutative Ring Theory. Cambridge University Press, 1989. | MR | Zbl

[26] H. Matsumura. - Formal power series rings over polynomial rings I. In Number Theory, Algebraic Geometry and Commutative Algebra. Kinokuniya, 1973, pp. 511-520. In honor of Y. Akizuki. | MR | Zbl

[27] F. Mehlmann. - Ein Beweis für einen Satz von Raynaud über flache Homomorphismen affinoider Algebren. - Schr. Math. Inst. Univ. Munster, 2 (1981). | MR | Zbl

[28] M. Nagata. - Local Rings. Interscience Publishers, 1962. | MR | Zbl

[29] Z. Robinson. - Smooth points of $p$ -adic subanalytic sets. Manuscripta Math., 80 (1993) 45-71. | DOI | EuDML | MR | Zbl

[30] Z. Robinson. - Flatness and smooth points of $p$ -adic subanalytic sets. Ann. Pure Appl. Logic, 88 (1997) 217-225. | DOI | MR | Zbl

[31] Z. Robinson. - A rigid analytic approximation theorem. This volume.

[32] H. Schoutens. - Rigid subanalytic sets. Comp. Math., 94 (1994) 269-295. | EuDML | Numdam | MR | Zbl

[33] H. Schoutens. - Rigid subanalytic sets in the plane. J. Algebra, 170 (1994) 266-276. | DOI | MR | Zbl

[34] H. Schoutens. - Uniformization of rigid subanalytic sets. Comp. Math., 94 (1994) 227-245. | EuDML | Numdam | MR | Zbl

[35] H. Schoutens. - Blowing up in rigid analytic geometry. Bull. Belg. Math. Soc, 2 (1995) 399-417. | EuDML | MR | Zbl

[36] H. Schoutens. - Closure of rigid semianalytic sets. J. Algebra, 198 (1997) 120-134. | DOI | MR | Zbl

[37] H. Schoutens. - Rigid analytic flatificators. Preprint. | DOI | MR | Zbl

[38] H. Seydi. - Sur une note d'Ernst Kunz. C. R. Acad. Sci. Paris, Ser. A-B, 274 (1972) A714-A716. | MR | Zbl

[39] J. Tate. - Rigid analytic spaces. Invent. Math., 12, (1971) 257-289. | DOI | EuDML | MR | Zbl

[40] V. Weispfenning. - Quantifier Elimination and Decision Procedures for Valued Fields. In Models and Sets, Aachen, 1983. Lecture Notes in Math., 1103 (1984) 419-472. Springer-Verlag. | MR | Zbl

[41] O. Zariski and P. Samuel. - Commutative Algebra II. Springer-Verlag, 1975. | MR | Zbl