Module de congruences pour GL(2) d'un corps imaginaire quadratique et th' eorie d'Iwasawa d'un corps CM biquadratique, by Eric Urban

This paper has appeared in Duke Math. J. 92 (1998), no. 1, 179-220, and so the dvi version has been removed. Let K be an imaginary quadratic field. In this paper, we prove a very closed relation between the Iwasawa theory of a quadratic extension M of K and the congruence module associated with a p-adic family of modular forms for GL(2,K) obtained by theta lift from Hecke characters of M. Comparing our method with the works of Hida-Tilouine, we conjecture a surprising relation between a congruence module for GL(2) for the real subfield of M and GL(2,K).

Eric Urban <urban@math.univ-paris13.fr>