Grothendieck’s existence theorem in analytic geometry and related results
HTML articles powered by AMS MathViewer
- by Siegmund Kosarew PDF
- Trans. Amer. Math. Soc. 328 (1991), 259-306 Request permission
Abstract:
We state and prove several kinds of analytification theorems of formal objects (such as coherent sheaves and formal complex spaces) which are in the spirit of Grothendieck’s algebraization theorem in [EGA, III]. The formulation of the results was derived from deformation theory and especially M. Artin’s work on representability of functors. The methods of proof depend heavily on a deeper study of cotangent complexes and resolvants. As applications one can deduce the convergence of formal versal deformations in diverse situations.References
- M. Artin, Algebraization of formal moduli. I, Global Analysis (Papers in Honor of K. Kodaira), Univ. Tokyo Press, Tokyo, 1969, pp. 21–71. MR 0260746
- Jürgen Bingener, Über formale komplexe Räume, Manuscripta Math. 24 (1978), no. 3, 253–293 (German). MR 492367, DOI 10.1007/BF01167833
- Jürgen Bingener, Darstellbarkeitskriterien für analytische Funktoren, Ann. Sci. École Norm. Sup. (4) 13 (1980), no. 3, 317–347 (German). MR 597743
- Jürgen Bingener, Offenheit der Versalität in der analytischen Geometrie, Math. Z. 173 (1980), no. 3, 241–281 (German). MR 592373, DOI 10.1007/BF01159663 J. Bingener and S. Kosarew, Lokale Modulräume in der analytischen Geometrie, Aspects of Math., D2, D3, Vieweg-Verlag, Braunschweig, 1987.
- Adrien Douady, Le problème des modules pour les sous-espaces analytiques compacts d’un espace analytique donné, Ann. Inst. Fourier (Grenoble) 16 (1966), no. fasc. 1, 1–95 (French). MR 203082
- A. Douady, Le problème des modules locaux pour les espaces $\textbf {C}$-analytiques compacts, Ann. Sci. École Norm. Sup. (4) 7 (1974), 569–602 (1975) (French). MR 382729
- Hubert Flenner and Siegmund Kosarew, On locally trivial deformations, Publ. Res. Inst. Math. Sci. 23 (1987), no. 4, 627–665. MR 918518, DOI 10.2977/prims/1195176251
- Otto Forster and Knut Knorr, Konstruktion verseller Familien kompakter komplexer Räume, Lecture Notes in Mathematics, vol. 705, Springer, Berlin, 1979 (German). MR 529598
- J. Frisch, Aplatissement en géométrie analytique, Ann. Sci. École Norm. Sup. (4) 1 (1968), 305–312 (French). MR 236421 A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique, Inst. Hautes Études Sci. Publ. Math. 4, 8, 11, 17, 20, 24, 28, 32 (1960-1967).
- Donald Knutson, Algebraic spaces, Lecture Notes in Mathematics, Vol. 203, Springer-Verlag, Berlin-New York, 1971. MR 0302647
- Ernst Kunz, Kähler differentials, Advanced Lectures in Mathematics, Friedr. Vieweg & Sohn, Braunschweig, 1986. MR 864975, DOI 10.1007/978-3-663-14074-0
- V. P. Palamodov, Deformations of complex spaces, Uspehi Mat. Nauk 31 (1976), no. 3(189), 129–194 (Russian). MR 0508121 —, The tangent complex of an analytic space, Amer. Math. Soc. Transl. 122 (1984), 119-171.
- Geneviève Pourcin, Théorème de Douady au-dessus de $S$, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 23 (1969), 451–459 (French). MR 257402
- Yum Tong Siu and Günther Trautmann, Deformations of coherent analytic sheaves with compact supports, Mem. Amer. Math. Soc. 29 (1981), no. 238, iii+155. MR 597091, DOI 10.1090/memo/0238
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 328 (1991), 259-306
- MSC: Primary 32C35; Secondary 32G07, 32G13
- DOI: https://doi.org/10.1090/S0002-9947-1991-1014252-X
- MathSciNet review: 1014252