SÉMINAIRE DE THÉORIE DES NOMBRES 2001-2002
Le Vendredi à 15 heures 30 en Salle de Conférence Organisateur : Arnaud Jehanne |
ManchesterClass invariants, Iwasawa theory and elliptic curves.
RÉSUMÉ
We will discuss the class invariant homomorphism for some Hopf orders of arithmetic interest. This map gives a measure of the Galois structure of certain field extensions with prescribed ramification. In particular, we construct a tower of Hopf orders arising from the division points of a CM elliptic curve and give an explicit parametrization of the corresponding class invariants. Using this, and standard Iwasawa theory, we can relate the vanishing of the class invariants to the behaviour of a p-adic L-function associated to the curve.