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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2509.16695 |
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| _version_ | 1866908855680630784 |
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| author | Levy, Ishan Li, Guchuan Zhang, Ningchuan |
| author_facet | Levy, Ishan Li, Guchuan Zhang, Ningchuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16695 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Picard groups of quotient ring spectra Levy, Ishan Li, Guchuan Zhang, Ningchuan Algebraic Topology 14C22, 55P43 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. |
| title | Picard groups of quotient ring spectra |
| topic | Algebraic Topology 14C22, 55P43 |
| url | https://arxiv.org/abs/2509.16695 |