Deformations via Simplicial Deformation Complexes

Details Deformations via Simplicial Deformation Complexes Deformations via Simplicial Deformation Complexes

2003-11-11

arxiv.org/abs/math/0311168v6

Mathematics

Algebraic Geometry

59 pages; presentational changes, minor corrections & improvements; proofs shortened in final section;v5 new examples added; v

Scientific paper

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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