Hao Peng (MIT)

The Beilinson–Bloch–Kato conjecture generalizes the rank part of the Birch–Swinnerton–Dyer conjecture for elliptic curves. I will present a proof of the analytic rank-0 case for a broad class of polarized motives attached to conjugate self-dual cuspidal representations of GL(2r) over a CM field F. The method is automorphic: using theta correspondence together with local and global seesaw identities, we reduce the conjecture to another conjecture related to non-vanishing of Bessel periods on unitary groups in the Gan–Gross–Prasad framework. Similar trick works in the orthogonal setting. These results apply to odd symmetric powers of non-CM modular elliptic curves over totally real number fields.