| 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. |
