Infinitesimal lifting and Jacobi criterion for smoothness on formal schemes

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dc.creatorAlonso, Leovigildo
dc.creatorJeremias, Ana
dc.creatorPerez, Marta
dc.date2006-04-11
dc.date.accessioned2026-07-07T07:10:45Z
dc.date.available2026-07-07T07:10:45Z
dc.descriptionThis 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.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/math/0604241
dc.identifierhttp://arxiv.org/abs/math/0604241
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111521
dc.subjectAlgebraic Geometry
dc.subjectPrimary 14B10; Secondary 14B20, 14B25
dc.titleInfinitesimal lifting and Jacobi criterion for smoothness on formal schemes
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