Reference : Unramifiedness of weight one Hilbert Hecke algebras
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Physical, chemical, mathematical & earth Sciences : Mathematics
Unramifiedness of weight one Hilbert Hecke algebras
Deo, Shaunak []
Dimitrov, Mladen []
Wiese, Gabor mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
[en] We prove that the Galois pseudo-representation valued in the mod p^n parallel weight 1 Hecke algebra for GL(2) over a totally real number field F is unramified at a place above p if p-1 does not divide the ramification index at that place. A novel geometric ingredient is the construction and study, in the case when p ramifies in F, of generalised Theta-operators using Reduzzi-Xiao's
generalised Hasse invariants, including especially an injectivity criterion in terms of minimal weights.
Fonds National de la Recherche - FnR & Agence National de la Recherche (France): INTER/ANR/18/12589973

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