Iwasawa theoretic Gross-Zagier theorem

(Un exposé de Ben Howard au séminaire de théorie des nombres de Chevaleret le 6 mars 2006)

Résumé :

  Perrin-Riou has proved a p-adic form of the Gross-Zagier theorem, relating the p-adic height pairing of a Heegner point to the central derivative of the p-adic L-function of an elliptic curve. Mazur and Rubin have since given a conjectural generalization of this, in which the Heegner point is replaced by the inverse limit of Heegner points in an anticyclotomic tower, the p-adic height pairing is replaced by a pairing valued in the Iwasawa algebra, and the derivative of the p-adic L-function is replaced by the linear term of a two-variable p-adic L-function. I will sketch a proof of Mazur and Rubin's conjecture, and explain the connection with Perrin-Riou's Iwasawa main conjecture for Heegner points