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Integral models of Hilbert modular varieties in the ramified case, deformations of modular Galois representations, and weight one forms

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Abstract

We prove the strong Artin conjecture for continuous, totally odd, two-dimensional representations of the absolute Galois group of a totally real field F.

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Notes

  1. \({\mathrm {deg}}(C)\) is ‘normalised’ such that \({\mathrm {deg}}(C)=0\) (resp. f) if and only if C is multiplicative (resp. étale).

  2. The construction is often attributed to Demazure, Lusztig, Bott, Samelson and Hansen.

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  1. Fakultät für Mathematik, Universität Duisburg-Essen, Thea-Leymann-Str. 9, 45127, Essen, Germany

    Shu Sasaki

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Sasaki, S. Integral models of Hilbert modular varieties in the ramified case, deformations of modular Galois representations, and weight one forms. Invent. math. 215, 171–264 (2019). https://doi.org/10.1007/s00222-018-0825-x

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