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arXiv · 2402.17921

Model Structures on Infinity-Categories of Filtrations

Colin Aitken
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Abstract

In 1974, Gugenheim and May showed that the cohomology $\text{Ext}_A(R,R)$ of a connected augmented algebra over a field $R$ is generated by elements with $s = 1$ under matric Massey products. In particular, this applies to the $E_2$ page of the $H\mathbb{F}_p$-based Adams spectral sequence. By studying a novel sequence of deformations of a presentably symmetric monoidal stable $\infty$-category $C$, we show that for a variety of spectral sequences coming from filtered spectra, the set of elements on the $E_2$ page surviving to the $E_k$ page is generated under matric Massey products by elements with degree $s < k.$ This work is the author's PhD thesis, completed under the supervision of Peter May.

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Colin Aitken. 2024-02-27. Model Structures on Infinity-Categories of Filtrations. https://arxiv.org/abs/2402.17921

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