Endoscopy on $\mathrm{SL}_2$-eigenvarieties
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916167440924672 |
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| author | Johansson, Christian Ludwig, Judith |
| author_facet | Johansson, Christian Ludwig, Judith |
| contents | In this paper, we study p-adic endoscopy on eigenvarieties for $\mathrm{SL}_2$ over totally real fields, taking a geometric perspective. We show that non-automorphic members of endoscopic L-packets of regular weight contribute eigenvectors to overconvergent cohomology at critically refined endoscopic points on the eigenvariety, and we precisely quantify this contribution. This gives a new perspective on and generalizes previous work of the second author. Our methods are geometric, and are based on showing that the $\mathrm{SL}_2$-eigenvariety is locally a quotient of an eigenvariety for $\mathrm{GL}_2$, which allows us to explicitly describe the local geometry of the $\mathrm{SL}_2$-eigenvariety. In particular, we show that it often fails to be Gorenstein at such points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_03103 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Endoscopy on $\mathrm{SL}_2$-eigenvarieties Johansson, Christian Ludwig, Judith Number Theory In this paper, we study p-adic endoscopy on eigenvarieties for $\mathrm{SL}_2$ over totally real fields, taking a geometric perspective. We show that non-automorphic members of endoscopic L-packets of regular weight contribute eigenvectors to overconvergent cohomology at critically refined endoscopic points on the eigenvariety, and we precisely quantify this contribution. This gives a new perspective on and generalizes previous work of the second author. Our methods are geometric, and are based on showing that the $\mathrm{SL}_2$-eigenvariety is locally a quotient of an eigenvariety for $\mathrm{GL}_2$, which allows us to explicitly describe the local geometry of the $\mathrm{SL}_2$-eigenvariety. In particular, we show that it often fails to be Gorenstein at such points. |
| title | Endoscopy on $\mathrm{SL}_2$-eigenvarieties |
| topic | Number Theory |
| url | https://arxiv.org/abs/2205.03103 |