UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ATTACHED TO HILBERT MODULAR FORMS MOD OF WEIGHT 1
2018 ◽
Vol 19
(2)
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pp. 281-306
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Keyword(s):
The main result of this article states that the Galois representation attached to a Hilbert modular eigenform defined over $\overline{\mathbb{F}}_{p}$ of parallel weight 1 and level prime to $p$ is unramified above $p$. This includes the important case of eigenforms that do not lift to Hilbert modular forms in characteristic 0 of parallel weight 1. The proof is based on the observation that parallel weight 1 forms in characteristic $p$ embed into the ordinary part of parallel weight $p$ forms in two different ways per prime dividing $p$, namely via ‘partial’ Frobenius operators.
2009 ◽
Vol 145
(5)
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pp. 1081-1113
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2012 ◽
Vol 11
(3)
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pp. 659-693
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2013 ◽
Vol 142
(3-4)
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pp. 513-524
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2015 ◽
Vol 67
(4)
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pp. 893-922
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Keyword(s):
1997 ◽
Vol 1997
(491)
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pp. 199-216
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2006 ◽
Vol 117
(2)
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pp. 397-405
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Keyword(s):
1989 ◽
Vol 21
(1)
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pp. 65-70
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