Non-generic components of the Emerton-Gee stack for $\mathrm{GL}_2$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912287958237184 |
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| author | Kansal, Kalyani Savoie, Ben |
| author_facet | Kansal, Kalyani Savoie, Ben |
| contents | Let $K$ be a finite unramified extension of $\mathbb{Q}_p$ with $p > 3$. We study the extremely non--generic irreducible components in the reduced part of the Emerton--Gee stack for $\mathrm{GL}_2$. We show precisely which irreducible components are smooth, which are normal, and which have Gorenstein normalizations. We show that the normalizations of the irreducible components admit smooth--local covers by resolution--rational schemes. We also determine the singular loci on the components, and use our results to update expectations about the conjectural categorical $p$--adic Langlands correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07883 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-generic components of the Emerton-Gee stack for $\mathrm{GL}_2$ Kansal, Kalyani Savoie, Ben Number Theory 11S99 Let $K$ be a finite unramified extension of $\mathbb{Q}_p$ with $p > 3$. We study the extremely non--generic irreducible components in the reduced part of the Emerton--Gee stack for $\mathrm{GL}_2$. We show precisely which irreducible components are smooth, which are normal, and which have Gorenstein normalizations. We show that the normalizations of the irreducible components admit smooth--local covers by resolution--rational schemes. We also determine the singular loci on the components, and use our results to update expectations about the conjectural categorical $p$--adic Langlands correspondence. |
| title | Non-generic components of the Emerton-Gee stack for $\mathrm{GL}_2$ |
| topic | Number Theory 11S99 |
| url | https://arxiv.org/abs/2407.07883 |