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

Romyar Sharifi

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)251-300
Number of pages50
JournalAnnals of Mathematics
Issue number1
StatePublished - Jan 2011
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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