Deformations of schemes and other bialgebraic structures

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, we show how to construct a Simplicial Deformation Complex (SDC) governing any bialgebraic deformation problem. Examples of such problems are deformations of a Hopf algebra, or of an arbitrary scheme. In characteristic zero, SDCs and DGLAs are shown to be equivalent.