[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 :
In press
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
