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