Commutative formal groups arising from schemes

Abstract

We prove the following criterion for the pro-representability of the deformation cohomology of a commutative formal Lie group. Let f be a flat and separated morphism between noetherian schemes. Assume that the target of f is flat over the integers. For a commutative formal Lie group E, we have the deformation cohomology of f with coefficients in E at our disposal. If the higher direct images of the tangent space of E are locally free and of finite rank then the deformation cohomology is pro-representable by a commutative formal Lie group.