Deformations of schemes and other bialgebraic structures

Pridham, J.

doi:10.1090/S0002-9947-07-04355-3

Deformations of schemes and other bialgebraic structures
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by J. P. Pridham PDF

Trans. Amer. Math. Soc. 360 (2008), 1601-1629 Request permission

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, 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.

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