Unramifiedness of weight one Hilbert Hecke algebras
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arXiv
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| Format: | Preprint |
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2019
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| author | Deo, Shaunak V. Dimitrov, Mladen Wiese, Gabor |
| author_facet | Deo, Shaunak V. Dimitrov, Mladen Wiese, Gabor |
| contents | We prove that the Galois pseudo-representation valued in the mod $p^n$ cuspidal Hecke algebra for GL(2) over a totally real number field $F$, of parallel weight $1$ and level prime to $p$, is unramified at any place above $p$. The same is true for the non-cuspidal Hecke algebra at places above $p$ whose ramification index is not divisible by $p-1$. A novel geometric ingredient, which is also of an independent interest, is the construction and study, in the case when $p$ ramifies in $F$, of generalised $Θ$-operators using Reduzzi--Xiao's generalised Hasse invariants, including especially an injectivity criterion in terms of minimal weights. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1911_11196 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Unramifiedness of weight one Hilbert Hecke algebras Deo, Shaunak V. Dimitrov, Mladen Wiese, Gabor Number Theory 11F80 (primary), 11F25, 11F33, 11F41, 11G18, 14G35 We prove that the Galois pseudo-representation valued in the mod $p^n$ cuspidal Hecke algebra for GL(2) over a totally real number field $F$, of parallel weight $1$ and level prime to $p$, is unramified at any place above $p$. The same is true for the non-cuspidal Hecke algebra at places above $p$ whose ramification index is not divisible by $p-1$. A novel geometric ingredient, which is also of an independent interest, is the construction and study, in the case when $p$ ramifies in $F$, of generalised $Θ$-operators using Reduzzi--Xiao's generalised Hasse invariants, including especially an injectivity criterion in terms of minimal weights. |
| title | Unramifiedness of weight one Hilbert Hecke algebras |
| topic | Number Theory 11F80 (primary), 11F25, 11F33, 11F41, 11G18, 14G35 |
| url | https://arxiv.org/abs/1911.11196 |