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Transactions of the American Mathematical Society

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

 

 

Grothendieck's existence theorem in analytic geometry and related results


Author: Siegmund Kosarew
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
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1991-1014252-X
Article copyright: © Copyright 1991 American Mathematical Society