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Bulletin of the London Mathematical Society Advance Access originally published online on February 11, 2009
Bulletin of the London Mathematical Society 2009 41(1):147-154; doi:10.1112/blms/bdn117
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© 2009 London Mathematical Society

Reduction modulo p of cuspidal representations and weights in Serre's conjecture

Michael M. Schein

Einstein Institute of Mathematics
Hebrew University of Jerusalem
Givat Ram
Jerusalem 91904
Israel
Current address:
Department of Mathematics
Bar-Ilan University
Ramat Gan 52900
Israel
mschein@math.biu.ac.il

Received 10 March 2008. Revision received 23 September 2008.

Let O be the ring of integers of a p-adic field and p its maximal ideal. This paper computes the Jordan–Hölder decomposition of the reduction modulo p of the cuspidal representations of GL2(O/pe) for e ≥ 1. An alternative formulation of Serre's conjecture for Hilbert modular forms is then provided.

2000 Mathematics Subject Classification 11F80, 22E50.


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