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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.05462 |
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| _version_ | 1866911779220619264 |
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| author | Ardakov, Konstantin Wadsley, Simon J. |
| author_facet | Ardakov, Konstantin Wadsley, Simon J. |
| contents | Let $F$ be a finite extension of $\mathbb{Q}_p$, let $Ω_F$ be Drinfeld's upper half-plane over $F$ and let $G^0$ the subgroup of $GL_2(F)$ consisting of elements whose determinant has norm $1$. By working locally on $Ω_F$, we construct and classify the torsion $G^0$-equivariant line bundles with integrable connection on $Ω$ in terms of the smooth linear characters of the units of the maximal order of the quaternion algebra over $F$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05462 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Equivariant line bundles with connection on the p-adic upper half plane Ardakov, Konstantin Wadsley, Simon J. Number Theory Representation Theory 14G22, 14F10 Let $F$ be a finite extension of $\mathbb{Q}_p$, let $Ω_F$ be Drinfeld's upper half-plane over $F$ and let $G^0$ the subgroup of $GL_2(F)$ consisting of elements whose determinant has norm $1$. By working locally on $Ω_F$, we construct and classify the torsion $G^0$-equivariant line bundles with integrable connection on $Ω$ in terms of the smooth linear characters of the units of the maximal order of the quaternion algebra over $F$. |
| title | Equivariant line bundles with connection on the p-adic upper half plane |
| topic | Number Theory Representation Theory 14G22, 14F10 |
| url | https://arxiv.org/abs/2309.05462 |