Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584146 | Journal of Algebra | 2016 | 25 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Marta Pérez Rodríguez,