Geodesic
A reciprocity map and the two-variable $p$-adic $L$-function
Romyar Sharifi1
1 Department of Mathematics<br/>University of Arizona<br/> Tuscon, AZ 85721
Annals of mathematics, Tome 173 (2011) no. 1, pp. 251-300.

Voir la notice de l'article provenant de la source Annals of Mathematics website

For primes $p \ge 5$, 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.
DOI : 10.4007/annals.2011.173.1.7

Romyar Sharifi 1

1 Department of Mathematics<br/>University of Arizona<br/> Tuscon, AZ 85721 
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Romyar Sharifi. A reciprocity map and the two-variable $p$-adic $L$-function. Annals of mathematics, Tome 173 (2011) no. 1, pp. 251-300. doi : 10.4007/annals.2011.173.1.7. http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.173.1.7/

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