Infinitesimal lifting and Jacobi criterion for smoothness on formal schemes

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This a first step to develop a theory of smooth, etale and unramified morphisms between noetherian formal schemes. Our main tool is the complete module of differentials, that is a coherent sheaf whenever the map of formal schemes is of pseudo finite type. Among our results we show that these infinitesimal properties of a map of usual schemes carry over into the completion with respect to suitable closed subsets. We characterize unramifiedness by the vanishing of the module of differentials. Also we see that a smooth morphism of noetherian formal schemes is flat and its module of differentials is locally free. The paper closes with a version of Zariski's Jacobian criterion.
26 pages

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Algebraic Geometry, Primary 14B10; Secondary 14B20, 14B25

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http://salesiana.dossiersoluciones.com/handle/123456789/111521

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0604241
 http://arxiv.org/abs/math/0604241

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arXiv