Quillen's Fundamental Spectral Sequences Revisited
Abstract
Quillen's fundamental spectral sequences relate Andr\'{e}-Quillen homology and cohomology to Tor and Ext functors. The five-term exact sequences arising from these spectral sequences are leveraged to characterize regular and complete intersection local rings. Despite their immense importance in the theory of Andr\'{e}-Quillen homology and cohomology, these spectral sequences are not treated in the literature as they merit. A sketchy argument with gaps for a special case of the first spectral sequence appears in an unpublished manuscript of Quillen, while the second spectral sequence is only stated without proof in another paper of Quillen. A rigorous proof of the spectral sequences requires a delicate investigation of the subtle structures involved. The goal of this expository article is to present a comprehensive and detailed proof of Quillen's fundamental spectral sequences in a readable and well-structured manner.
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Cite
@article{arxiv.2405.04709,
title = {Quillen's Fundamental Spectral Sequences Revisited},
author = {Hossein Faridian},
journal= {arXiv preprint arXiv:2405.04709},
year = {2024}
}