Anticyclotomic Euler systems for conjugate self-dual representations of $GL(2n)$

Abstract: An Euler system is a collection of Galois cohomology classes which satisfy certain compatibility relations under corestriction, and by constructing an Euler system and relating the classes to $L$-values, one can establish instances of the Bloch--Kato conjecture. In this talk, I will describe a construction of an anticyclotomic Euler system for a certain class of conjugate self-dual automorphic representations, which can be seen as a generalisation of the Heegner point construction. The classes arise from special cycles on unitary Shimura varieties and are closely related to the branching law associated with the spherical pair $(GL(n) \times GL(n), GL(2n))$. This is joint work with S.W.A. Shah.

number theory

Audience: researchers in the topic

London number theory seminar

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