Hilbert modular forms and p-adic Hodge theory
By Takeshi Saito. Compositio Mathematica, 2006
72 citations recorded by the source corpus.
Abstract For the p-adic Galois representation associated to a Hilbert modular form, Carayol has shown that, under a certain assumption, its restriction to the local Galois group at a finite place not dividing p is compatible with the local Langlands correspondence. Under the same assumption, we show that the same is true for the places dividing p, in the sense of p-adic Hodge theory, as is shown for an elliptic modular form. We also prove that the monodromy-weight conjecture holds for such representations.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7635de8e2d45a83922c337e204874feb4466f52e
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In Geometry and Topology
- Jean-Pierre Wintenberger
- Lassina Dembélé
- John Voight
- Chandrashekhar B. Khare
- John Cremona
- J. Thorne
- Frank Calegari
- James Newton
In Mathematical Physics
- Jean-Pierre Wintenberger
- Lassina Dembélé
- John Voight
- Chandrashekhar B. Khare
- John Cremona
- J. Thorne
- Frank Calegari
- James Newton
Citations in the corpus
- Explicit Methods for Hilbert Modular Forms (2010, result): “The existence of this representation is due to work of Blasius-Rogawski [2], Carayol [6], Deligne [13], Saito [51], Taylor [65], and Wiles [72].”
- Serre’s modularity conjecture (II) (2009, background): “The compatibility at all places follows from [7], [29],[30],[33].”