NTS ABSTRACTFall2025

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Oct 16

Qiao He (Columbia)

Oct 30

Beilinson-Bloch-Kato conjecture for polarized motives

Hao Peng (MIT)

The Beilinson—Bloch—Kato conjecture is a far-fetching generalization of the (rank part of the) BSD conjecture for modular elliptic curves. The conjecture is partially proved for U(N)*U(N+1)-motives in the work of Y. Liu, Y. Tian, L. Xiao, W. Zhang, and X. Zhu. Using theta correspondence, we prove that their result implies the BBK conjecture for U(2n)-motives, e.g. odd symmetric powers of non-CM modular elliptic curves, in the rank zero case. Similar trick works in the orthogonal case. If time permits, we talk about the work in progress partiallu proving the BBK conjecture for O(N)*O(N+1)-motives when analytic rank is at most one.