A reciprocity map and the two-variable p-adic L-function

作者：Sharifi Romyar^*

来源：Annals of Mathematics, 2011, 173(1): 251-300.

DOI：10.4007/annals/2011.173.1.7

For primes p >= 5, we propose a conjecture that relates the values of cup products in the Galois cohomology of the maximal unramified outside p extension of a cyclotomic field on cyclotomic p-units to the values of p-adic L-functions of cuspidal eigenforms that satisfy mod p congruences with Eisenstein series. Passing up the cyclotomic and Hida towers, we construct an isomorphism of certain spaces that allows us to compare the value of a reciprocity map on a particular norm compatible system of p-units to what is essentially the two-variable p-adic L-function of Mazur and Kitagawa.

• 出版日期2011-1