Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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


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.
  • 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
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 32C35, 32G07, 32G13
  • Retrieve articles in all journals with MSC: 32C35, 32G07, 32G13
Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 328 (1991), 259-306
  • MSC: Primary 32C35; Secondary 32G07, 32G13
  • DOI:
  • MathSciNet review: 1014252