Reference : Higher congruence companion forms
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/11486
Higher congruence companion forms
English
Adibhatla, Rajender mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Oct-2012
Acta Arithmetica
Seminarjum Matematyczne Uniwersytetu
156
2
17
Yes
International
0065-1036
1730-6264
Warszawa
Poland
[en] modular forms ; Galois representations
[en] For a rational prime p≥3 we consider p-ordinary, Hilbert modular newforms f of weight k≥2 with associated p-adic Galois representations \rho_f and mod p^n reductions \rho_{f,n}. Under suitable hypotheses on the size of the image, we use deformation theory and modularity lifting to show that if the restrictions of \rho_{f,n} to decomposition groups above p split then f has a companion form g modulo pn (in the sense that \rho_{f,n} \sim \rho_{g,n}\otimes \chi^{k−1}).
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/11486
10.4064/aa156-2-4
http://arxiv.org/abs/1007.0181
The original publication is available at http://journals.impan.gov.pl/aa/

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