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

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

2007-09-22

arxiv.org/abs/0709.3591v3

Ann. of Math. 173 (2011) 251-300

Mathematics

Number Theory

55 pages

Scientific paper

For primes p greater than 3, 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.

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