Windows for cdgas

We study a Fourier-Mukai kernel associated to GIT wall-crossing for arbitrarily singular (not necessarily reduced or irreducible) affine varieties over any field. This is closely related derived fiber product diagram the and simple understand from viewpoint of commutative differential graded algebras. However, perspective algebraic varieties, can be quite complicated, corresponding complex with multiple homology sheaves. Under mild assumptions in Calabi-Yau case, we prove that this provides an equivalence between category perfect complexes on two quotients. More generally, obtain semi-orthogonal decompositions which show these categories differ by certain number copies fixed locus. The Mukai flop recovered as very special case.