Title: Constructing Split Kolyvagin Systems from Special Cycles on Unitary Groups
Speaker: Dimitar Jetchev (EPFL)
Time: 2019-3-27, 10:00-11:00
Place: MCM;110
Abstract: In this lecture, we will apply the formalism of split Kolyvagin systems from the previous lecture to specific cases such as the twist of an elliptic curve by a Hecke character of an imaginary quadratic field, or the more general setting of conjugate-dual Galois representations arising in the context of the Gan--Gross--Prasad conjectures for unitary groups. In these cases, we will show how one can construct split Kolyvagin systems establishing sufficiently many norm relations (without Euler systems congruence relations) and what the consequences of these are on the Bloch--Kato conjecture in this setting. The latter uses very recent results of Reda Boumasmoud. Different aspects of this work are joint with various people including Reda Boumasmoud, Hunter Brooks, Jan Nekovar, Chris Skinner.