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arXiv · 2509.16695

Picard groups of quotient ring spectra

Ishan Levy·Guchuan Li·Ningchuan Zhang
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Abstract

We develop tools to study Picard groups of quotients of ring spectra by a finitely generated ideal, which we use to show that $\mathrm{Pic}(\mathrm{E}_n/I) = \mathbb{Z}/2$, where $\mathrm{E}_n$ is a Lubin--Tate theory and $I$ is an ideal generated by suitable powers of a regular sequence. We apply this to obtain spectral sequences computing Picard groups of $\mathrm{K}(n)$-local generalized Moore algebras, and make some preliminary computations including the height $1$ case.

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Ishan Levy, Guchuan Li, Ningchuan Zhang. 2025-09-20. Picard groups of quotient ring spectra. https://doi.org/10.1112/topo.70093

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