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On Galois representations associated to Hilbert modular forms. II. (English) Zbl 0836.11017
Coates, John (ed.) et al., Elliptic curves, modular forms, & Fermat’s last theorem. Proceedings ot the conference on elliptic curves and modular forms held at the Chinese University of Hong Kong, December 18-21, 1993. Cambridge, MA: International Press. Ser. Number Theory. 1, 185-191 (1995).
The author studies the $$p$$-adic Galois representations associated to Hilbert modular forms. It is shown that for almost all $$p$$ these representations are crystalline at $$p$$. Many cases had already been settled by Carayol and Blasius/Rogawski. For the remainder the $$p$$-adic representations correspond to $$p$$-divisible groups.
For the entire collection see [Zbl 0824.00025].
Reviewer: G.Faltings (Bonn)

##### MSC:
 11F41 Automorphic forms on $$\mbox{GL}(2)$$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces 11F80 Galois representations