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

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

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
Volume173
Issue number1
DOIs
StatePublished - Jan 2011

Fingerprint

P-adic L-function
Cyclotomic
Reciprocity
Galois Cohomology
Cup Product
Cyclotomic Fields
Eisenstein Series
Unit
Congruence
Isomorphism
Norm

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

A reciprocity map and the two-variable p-adic L-function. / Sharifi, Romyar T.

In: Annals of Mathematics, Vol. 173, No. 1, 01.2011, p. 251-300.

Research output: Contribution to journalArticle

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