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

Fuente: arXiv
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Main Author: Leeman, Ethan
Format: Preprint
Published: 2025
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author Leeman, Ethan
author_facet Leeman, Ethan
contents André 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 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. 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.
format Preprint
id arxiv_https___arxiv_org_abs_2507_06099
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Andre-Quillen (co)homology and Equivariant Stable Homotopy Theory
Leeman, Ethan
Algebraic Topology
André 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 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. 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.
title Andre-Quillen (co)homology and Equivariant Stable Homotopy Theory
topic Algebraic Topology
url https://arxiv.org/abs/2507.06099