Deformations via Simplicial Deformation Complexes
代数几何
2007-05-23 v6
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.
引用
@article{arxiv.math/0311168,
title = {Deformations via Simplicial Deformation Complexes},
author = {J. P. Pridham},
journal= {arXiv preprint arXiv:math/0311168},
year = {2007}
}
备注
59 pages; presentational changes, minor corrections & improvements; proofs shortened in final section;v5 new examples added; v6 minor correction