Andre-Quillen (co)homology and equivariant stable homotopy theory

Andre and Quillen introduced a (co)homology theory for augmented commutative rings. Strickland [31] initially proposed some issues with the analogue of the abelianization functor in the equivariant setting. These were resolved by Hill [15] who further gave the notion of a genuine derivation and a module of Kähler differentials. We build on this endeavor by expanding to incomplete Tambara functors, introducing the cotangent complex and its various properties, and producing an analogue of the fundamental spectral sequence.