Non-abelian congruences between p-adic L-functions.

(Attention, horaire exceptionnel : 17h)

Various people have conjectured the existence of non-abelian
p-adic L-functions attached to elliptic curves. K. Kato reduced
the proof of existence into a family of congruences
amongst Artin twists of the Hasse-Weil L-functions. We prove forms
of these congruences using the theory of Hilbert modular forms.