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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Grothendieck’s existence theorem in analytic geometry and related results
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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.
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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