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

By R. Sharifi. 2007

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For primes p 5, we propose a conjecture that relates the values of cup products in the Galois cohomology of the maximal unramied outside p extension of a cyclotomic eld 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1e1d1614bcdf009355eb658a35b6f5379c79e849