Andre-Quillen (co)homology and Equivariant Stable Homotopy Theory

Abstract

Andr\'e and Quillen introduced a (co)homology theory for augmented commutative rings. Strickland initially proposed some issues with the analogue of the abelianization functor in the equivariant setting. These were resolved by Hill who further gave the notion of a genuine derivation and a module of K\"ahler 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. Note: This thesis is reposted with a correction that appears at the end of chapter 3. Namely, we make an additional assumption that a map be a cofibration in order to generate the transitivity long exact sequence. This change influences chapter 4 and when we can generate the fundamental spectral sequence.