Unramifiedness of weight one Hilbert Hecke algebras

[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.

Disciplines :

Mathematics

Author, co-author :

Deo, Shaunak

Dimitrov, Mladen

WIESE, Gabor ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit

External co-authors :

yes

Language :

English

Title :

Unramifiedness of weight one Hilbert Hecke algebras

Publication date :

2024

Journal title :

Algebra and Number Theory

ISSN :

1937-0652

eISSN :

1944-7833

Publisher :

Mathematical Sciences Publishers, Berkeley, United States - California

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

Fonds National de la Recherche - FnR & Agence National de la Recherche (France): INTER/ANR/18/12589973

Available on ORBilu :

since 26 November 2019

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Bibliography

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