The Bloch--Kato conjecture for conjugate self-dual automorphic representations

Given a p-adic Galois representation, the Bloch--Kato conjecture predicts a relation between the order of vanishing of its complex L-function and the dimension of its Bloch--Kato Selmer group. In this talk I will describe ongoing work towards proving cases of this conjecture for Galois representations associated with conjugate self-dual automorphic representations of GL(2n) satisfying various hypotheses (e.g. odd symmetric powers of elliptic curves). The main ingredients are the construction of an Euler system and a p-adic L-function relating the Euler system to special values of the complex L-function.