## Murilo Corato Zanarella : First explicit reciprocity law for unitary Friedbergâ??Jacquet periods

- Number Theory ( 0 Views )In the early 2000's, Bertolini and Darmon introduced a new technique to bound Selmer groups of elliptic curves via level raising congruences. This was the first example of what is now termed a "bipartite Euler system", and over the last decade we have seen many breakthroughs on constructing such systems for other Galois representations, including settings such as twisted and cubic triple product, symmetric cube, and Rankinâ??Selberg, with applications to the Blochâ??Kato conjecture and to Iwasawa theory. For this talk, I'll consider Galois representations attached to automorphic forms on a totally definite unitary group U(2r) over a CM field which are distinguished by the subgroup U(r) x U(r). I'll discuss a new "first explicit reciprocity law" in this setting and its application to the corresponding Blochâ??Kato conjecture, focusing on new obstacles which arise from the lack of local multiplicity one.