Séminaire TNGA : Andrew Graham

Orateur : Andrew Graham (Oxford)

Titre : Explicit reciprocity laws for unitary Friedberg–Jacquet cycles

Résumé : Unitary Friedberg–Jacquet (UFJ) periods generalise the toric periods appearing in Waldspurger’s formula, and are closely related to central L-values of symplectic-type cuspidal automorphic representations over CM fields. For certain choices of signatures, the unitary groups which appear in these periods give rise to special cycles on unitary Shimura varieties, generalising the construction of Heegner points.

In this talk, I will discuss an explicit reciprocity law relating values of a p-adic L-function (interpolating UFJ periods) to the p-adic regulator of these special cycles. This generalises the formula of Bertolini–Darmon–Prasanna.