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

• 成果类型: Article
• 署名作者: Sharifi, Romyar
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.173.1.7
• 发表日期: 2011
• 页码: 251-300
• 关键词: special values; companion forms; COHOMOLOGY; MODULES; towers

摘要

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.