Deformation of formal schemes through local homology

JOURNAL OF ALGEBRA

卷:445

Article

Rodriguez, Marta Perez¹ 

[1] Univ Vigo, Dept Math, Escola Super Enxenreia Informat, E-32004 Orense, Spain

关键词: Formal scheme;    Cotangent complex;    Lifting;    Deformation;    Local homology;   

DOI  :  10.1016/j.jalgebra.2015.07.041

来源: Elsevier

【 摘 要 】

We define the cotangent complex of a morphism f: (sic) -> 113 of locally noetherian formal schemes as an object in the derived category D-((sic)) through local homology. We discuss its basic properties and establish the basics results of a deformation theory, providing a characterization of smooth and etale 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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free