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arXiv · 1911.11196

Unramifiedness of weight one Hilbert Hecke algebras

Shaunak V. Deo·Mladen Dimitrov·Gabor Wiese
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Abstract

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 $\Theta$-operators using Reduzzi--Xiao's generalised Hasse invariants, including especially an injectivity criterion in terms of minimal weights.

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Shaunak V. Deo, Mladen Dimitrov, Gabor Wiese. 2019-11-25. Unramifiedness of weight one Hilbert Hecke algebras. https://doi.org/10.2140/ant.2024.18.1465

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