Reference : On certain finiteness questions in the arithmetic of modular forms
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/19221
On certain finiteness questions in the arithmetic of modular forms
English
Kiming, Ian [University of Copenhagen]
Rustom, Nadim [University of Copenhagen]
Wiese, Gabor mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2016
Journal of the London Mathematical Society
London Mathematical Society
94
2
479-502
Yes (verified by ORBilu)
International
0024-6107
1469-7750
London
United Kingdom
[en] We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We link these finiteness statements with a question by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms. Specifically, we conjecture that, for fixed N, m, and prime p with p not dividing N, there is only a finite number of reductions modulo p^m of normalized eigenforms on \Gamma_1(N). We consider various variants of our basic finiteness conjecture, prove a weak version of it, and give some numerical evidence.
http://hdl.handle.net/10993/19221
10.1112/jlms/jdw045
http://jlms.oxfordjournals.org/cgi/content/full/jdw045?ijkey=W0QMjjze99Mhjev&keytype=ref

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