A local analogue of the ghost conjecture of Bergdall-Pollack
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866913694130110464 |
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| author | Liu, Ruochuan Truong, Nha Xuan Xiao, Liang Zhao, Bin |
| author_facet | Liu, Ruochuan Truong, Nha Xuan Xiao, Liang Zhao, Bin |
| contents | We formulate a local analogue of the ghost conjecture of Bergdall and Pollack, which essentially relies purely on the representation theory of GL_2(Q_p). We further study the combinatorial properties of the ghost series as well as its Newton polygon, in particular, giving a characterization of the vertices of the Newton polygon and proving an integrality result of the slopes. In a forthcoming sequel, we will prove this local ghost conjecture under some mild hypothesis and give arithmetic applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_15372 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A local analogue of the ghost conjecture of Bergdall-Pollack Liu, Ruochuan Truong, Nha Xuan Xiao, Liang Zhao, Bin Number Theory 11F33 (primary), 11F85 (secondary) We formulate a local analogue of the ghost conjecture of Bergdall and Pollack, which essentially relies purely on the representation theory of GL_2(Q_p). We further study the combinatorial properties of the ghost series as well as its Newton polygon, in particular, giving a characterization of the vertices of the Newton polygon and proving an integrality result of the slopes. In a forthcoming sequel, we will prove this local ghost conjecture under some mild hypothesis and give arithmetic applications. |
| title | A local analogue of the ghost conjecture of Bergdall-Pollack |
| topic | Number Theory 11F33 (primary), 11F85 (secondary) |
| url | https://arxiv.org/abs/2206.15372 |