  We study the differential graded Lie algebra of endomorphisms of the Koszul
resolution of a regular sequence on a unitary commutative $K$-algebra $R$ and
we prove that it is homotopy abelian over $K$, while it is generally not formal
over $R$. We apply this result to prove an annihilation theorem for
obstructions of (derived) deformations of locally complete intersection ideal
sheaves on projective schemes.
