First Explicit Reciprocity Law for Unitary Friedberg-Jacquet Periods

Explore a 59-minute lecture on the first explicit reciprocity law for unitary Friedberg-Jacquet periods, presented by Murilo Zanarella from John Hopkins University. Delve into the evolution of bipartite Euler systems, from Bertolini and Darmon's pioneering work on bounding Selmer groups of elliptic curves to recent breakthroughs in various Galois representation settings. Examine the speaker's research on Galois representations attached to automorphic forms on totally definite unitary groups U(2r) over CM fields, distinguished by the subgroup U(r) x U(r). Gain insights into the new first explicit reciprocity law in this context and its application to the Bloch-Kato conjecture, with a focus on challenges arising from the absence of local multiplicity one.

First Explicit Reciprocity Law for Unitary Friedberg—Jacquet PeriodsMurilo Zanarella