Algebraic cycles and p-adic L-functions for conjugate-symplectic motives

Abstract: I will introduce ‘canonical’ algebraic cycles for motives $M$ enjoying a certain symmetry - for instance, some symmetric powers of elliptic curves. The construction is based on works of Kudla and Liu on some (conjecturally modular) theta series valued in Chow groups of Shimura varieties. The cycles have Heegner-point-like features that allow, under some assumptions, to support an analogue of the BSD conjecture for M at an ordinary prime $p$. Namely: if the $p$-adic $L$-function of $M$ vanishes at the center to order exactly 1, then the ${\bf Q}_p$-Selmer group of $M$ has rank 1, and it is generated by classes of algebraic cycles. Partly joint work with Yifeng Liu.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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