# Séminaires : Séminaire Théorie des Nombres

 Equipe(s) : fa, tn, tga, Responsables : Marc Hindry, Bruno Kahn, Wieslawa Niziol, Cathy Swaenepoel Email des responsables : cathy.swaenepoel@imj-prg.fr Salle : Adresse : Description http://www.imj-prg.fr/tn/STN/stnj.html

 Orateur(s) Romyar Sharifi - , Titre Reciprocity maps and Selmer groups Date 05/10/2009 Horaire 14:00 à 16:00 Diffusion Résume We will define and discuss the $S$-reciprocity map for a number field $F$, where $S$ is a set of primes of F containing those over a fixed primep. This is essentially a map from the S-units of F to a tensorproduct of pro-$p$ abelian Galois groups with restricted ramification.Particular attention will be paid to its relationship with cupproducts and with Selmer groups (or complexes) of residualrepresentations. For certain cyclotomic fields $F$, we will use this to suggest a connection with reductions of the $p$-adic $L$-functions ofcuspidal eigenforms that satisfy mod $p$ congruences with Eisensteinseries. Salle Adresse