通过单纯变形复合体的变形
Deformations via Simplicial Deformation Complexes
摘要：
长期以来，人们一直认为特征为零的变形问题都应该由一个微分分次李代数（DGLA）来处理。本文发展了单纯形变形复合体理论，作为DGLAs的替代。这些工作在所有的特点，并为许多问题可以构建规范。特别是，SDCs构造变形的任意计划，变形的霍普夫代数，变形的基本群的表示的问题。在零特征下，SDCs和DGLA是等价的。
英文摘要：
There has long been a philosophy that every deformation problem in characteristic zero should be governed by a differential graded Lie algebra (DGLA). In this paper, the theory of Simplicial Deformation Complexes (SDCs) is developed, as an alternative to DGLAs. These work in all characteristics, and for many problems can be constructed canonically. In particular, SDCs are constructed for the problems of deforming an arbitrary scheme, of deforming a Hopf algebra, and of deforming a representation of the fundamental group. In characteristic zero, SDCs and DGLAs are equivalent.
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