arXiv math/06042412006-04-11math.AG

Infinitesimal lifting and Jacobi criterion for smoothness on formal schemes

Leovigildo Alonso, Ana Jeremias, Marta Perez

备注：: 26 pages

英文摘要：

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.

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