形变理论综述(二):同伦方法

Review of Deformation Theory Ⅱ:A Homotopical Approach

本文从Hinich,Manetti和Pridham在同伦代数上的结果出发,给出形变理论的一个通用方法.特别地,我们证明所有特征为0的形变函子被一个同伦意义下特定的分次李代数控制,同时对任意特征的形变函子给出了非交换的类似结果.

We give a general treatment of deformation theory from the point of view of homotopical algebra following Hinich,Manetti and Pridham.In particular,we show that any deformation functor in characteristic zero is controlled by a certain differential graded Lie algebra defined up to homotopy,and also formulate a noncommutative analogue of this result valid in any characteristic.