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