Article ID Journal Published Year Pages File Type
4584146 Journal of Algebra 2016 25 Pages PDF
Abstract

We define the cotangent complex of a morphism f:X→Yf:X→Y of locally noetherian formal schemes as an object in the derived category D−(X)D−(X) through local homology. We discuss its basic properties and establish the basics results of a deformation theory, providing a characterization of smooth and étale morphisms. This leads to simpler lifting results depending on a differential module, for a class of non-smooth morphism of usual schemes. We also give descriptions of the cotangent complex in the case of regular closed immersions and complete intersection morphisms of formal schemes.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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