Jacobi-Bernoulli cohomology and deformations of schemes and maps

We introduce a notion of Jacobi-Bernoulli cohomology associated to a semi-simplicial Lie algebra (SELA). For an algebraic scheme $X$ over $\text{C}$, we construct a tangent SELA ${\text{t}}_X$ and show that the Jacobi-Bernoulli cohomology of ${\text{t}}_X$ is related to infinitesimal deformations of $X$.